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DC Circuits - Practice Questions (37)

Question 1: 2. As shown in the figure, the resistors $R _ { 1 } , R _ { 2 }$ of $I - U _ { \text {图像,把 } } R _ {...

2. As shown in the figure, the resistors $R _ { 1 } , R _ { 2 }$ of $I - U _ { \text {图像,把 } } R _ { 1 } , R _ { 2 }$ are connected in parallel to the circuit, and the current through them is ${ } ^ { I _ { 1 } } , I _ { 2 }$, respectively, then the following statements are correct ( ) ![](/images/questions/phys-dc-circuits/image-001.jpg)

  • A. A. $R _ { 1 } > R _ { 2 } , I _ { 1 } > I _ { 2 }$
  • B. B. $R _ { 1 } < R _ { 2 } , I _ { 1 } < I _ { 2 }$
  • C. C. $R _ { 1 } < R _ { 2 } , I _ { 1 } > I _ { 2 }$
  • D. D. $R _ { 1 } > R _ { 2 } , I _ { 1 } < I _ { 2 }$

Answer: D

Solution: $I - U _ { \text {图像的斜率表示电阻的倒数,所以 } } R _ { 1 } > R _ { 2 }$. Since the two resistors are connected in parallel, the voltages across the resistors are equal, and according to $I = \frac { U } { R }$, we can get $I _ { 1 } < I _ { 2 }$.

Question 2: 3. The rated voltage of a small bulb is 3 V, its volt-ampere characteristic curve shown in the figur...

3. The rated voltage of a small bulb is 3 V, its volt-ampere characteristic curve shown in the figure. The resistance of the small bulb when it glows normally is ![](/images/questions/phys-dc-circuits/image-002.jpg)

  • A. A. $15 \Omega$
  • B. B. $30 \Omega$
  • C. C. $0.07 \Omega$
  • D. D. $0.03 \Omega$

Answer: A

Solution: The rated voltage of the small bulb is 3 V , and according to the image, the rated current 0.2 A , so the $$ R = \frac { U } { I } = 15 \Omega $$

Question 3: 4. As shown in the figure, is a crystal diode volt-ampere characteristic curve, the following statem...

4. As shown in the figure, is a crystal diode volt-ampere characteristic curve, the following statements are correct ![](/images/questions/phys-dc-circuits/image-003.jpg)

  • A. A. When a forward voltage is added, the diode resistance is small and increases with increasing voltage
  • B. B. When a reverse voltage is added, the diode resistance is large and the current is small no matter how much voltage is added
  • C. C. Whether you add a forward voltage or a reverse voltage, the voltage and current are not proportional, so the diode is a nonlinear component
  • D. D. When a forward voltage is applied to a diode, the graph line of current versus voltage is a straight line

Answer: C

Solution: A. As can be seen from the figure, the slope indicates the reciprocal of the resistance, plus positive voltage, with the increase in voltage resistance becomes smaller, so A error; B. From the figure, add the reverse voltage, the diode resistance is larger, when the reverse voltage reaches a certain value, the diode will be broken, the current will become larger, so B error; C. As can be seen from the figure, the slope represents the reciprocal of the resistance, and in the change, so whether it is to add forward voltage or reverse voltage, voltage and current are not proportional, so the diode is a non-linear component, so C is correct; D. diode plus forward voltage, the current with the voltage change graph line is a curve, so D is wrong.

Question 4: 5. Under the action of a constant electric field, the metal conductor free electrons to do direction...

5. Under the action of a constant electric field, the metal conductor free electrons to do directional movement, in the process of movement with the conductor within the immobile particles continue to collide, collision impeded the directional movement of free charge, the result is that a large number of free electrons directional movement of the average rate does not change with time, this microscopic impediment to the macro-formation of the resistance. Four fixed-value resistors $a$, $b , c , d$ were connected to the circuit, the corresponding current and voltage values were measured as shown in the figure, which is the closest to the value of the two resistors are ![](/images/questions/phys-dc-circuits/image-004.jpg)

  • A. A. $a$ and $b$
  • B. B. $b$ and $d$
  • C. C. $a$ and $c$
  • D. D. $c$ and $d$

Answer: C

Solution: In the U-I image, the slope of the graph line indicates the resistance value of the resistor, so the two resistors with the closest resistance values are $a$ and c

Question 5: 6. As shown in Figure A, the circuit, the small bulb is energized after its voltage $U$ with the add...

6. As shown in Figure A, the circuit, the small bulb is energized after its voltage $U$ with the added current $I$ change of the graph line as shown in Figure B, $P$ for the graph line, $P N$ for the tangent to the line, $P M$ for the $U$ axis, $U$ is the plumb line, $P Q$ for the $U$ axis, $U$ is the plumb line. [INLINE_FORMULA_4]] is the vertical line of the $U$ axis, and $P Q$ is the vertical line of the $I$ axis. ![](/images/questions/phys-dc-circuits/image-005.jpg) A ![](/images/questions/phys-dc-circuits/image-006.jpg) B

  • A. A. As the applied current increases, the resistance of the small bulb increases
  • B. B. Corresponding to point $P$, the resistance of the small bulb is $R = \frac { U _ { 1 } } { I _ { 2 } }$
  • C. C. In a circuit where the voltage across bulb L is $U _ { 1 }$, the voltage across resistor $R$ is $I _ { 1 } R$.
  • D. D. Corresponding to the point $P$, the power of the small bulb is the "area" surrounded by the rectangle $P Q O M$ in the figure.

Answer: C

Solution: A. Points on the graph line and the origin of the slope of the line is equal to the size of the resistance, by the mathematical knowledge can be known, with the increase in the added voltage, the added current increases, the resistance of the small bulb increases, so A is correct; B. Corresponding to $P$ point, the resistance of the bulb is $$ R = \frac { U _ { 1 } } { I _ { 2 } } $$ Therefore, B is correct; C. When the voltage across bulb L in the circuit is $U _ { 1 }$, the voltage across resistor $R$ is $I _ { 2 } R$, so C is wrong; D. By the constant current power formula $P = U I$, promotion can be known, corresponding to the $P$ point, the power of the small bulb for the rectangle $P Q O M$ in the figure of the area surrounded by, so D is correct;

Question 6: 7. The following statements about electric current are correct ( )

7. The following statements about electric current are correct ( )

  • A. A. The current is a vector.
  • B. B. The direction of the current is the same as the direction of the directional movement of the electrons
  • C. C. The magnitude of current in a conductor of constant resistance is proportional to the voltage
  • D. D. The magnitude of the current in a conductor is proportional to the amount of electricity passing through the cross section of the conductor

Answer: C

Solution: A. Current is a scalar quantity, so A is wrong; B. The direction of the specified current is the same as the direction of positive charge movement and opposite to the direction of negative charge movement, so B is wrong; C. According to Ohm's law $$ I = \frac { U } { R } $$ it is known that the magnitude of the current in a conductor of constant resistance is proportional to the voltage, so C is correct; D. According to the defining equation of current $$ I = \frac { q } { t } $$ The current in a conductor is proportional to the amount of electricity that passes through the cross-section of the conductor per unit time, so D is wrong;

Question 7: 8. In the circuit shown in the figure, $R _ { 0 }$ is a constant-value resistor, $R$ is a sliding va...

8. In the circuit shown in the figure, $R _ { 0 }$ is a constant-value resistor, $R$ is a sliding varistor, and the total resistance of the circuit changes when the sliding contact $P$ is slid, the following is correct ( ) ![](/images/questions/phys-dc-circuits/image-007.jpg)

  • A. A. $P$ Slide to the left, total resistance becomes smaller
  • B. B. $P$ slides to the right, total resistance becomes smaller
  • C. C. $P$ When sliding to the leftmost end, the total resistance is $R _ { 0 }$
  • D. D. $P$ sliding to the rightmost end, the total resistance is $R$

Answer: A

Solution: AC. $P$ slides to the left, $R$ access to the circuit resistance decreases, the total resistance decreases, when the slide varistor slides the leftmost end, $R$ access to the circuit resistance is 0, the total resistance of the circuit is 0, A is correct, C is wrong; When $\mathrm { BD } . P$ slides to the right, $R$ increases the resistance of the circuit, and the total resistance increases, and when the sliding varistor slides to the rightmost end, $R$ When the sliding varistor is slid to the rightmost end, $R$ is connected to the circuit at the maximum value of $R$, and according to the parallel relationship of the resistors, the total resistance of the whole circuit is $\frac { R R _ { 0 } } { R + R _ { 0 } }$, and BD is wrong.

Question 8: 9. As shown in the figure is the volt-ampere characteristic curve of a conductor, the following stat...

9. As shown in the figure is the volt-ampere characteristic curve of a conductor, the following statements are correct () ![](/images/questions/phys-dc-circuits/image-008.jpg)

  • A. A. When the voltage across the conductor is 4 V, the resistance of the conductor is $10 \Omega$
  • B. B. When the voltage across the conductor is 4 V, the resistance of the conductor is $0.1 \Omega$
  • C. C. When the voltage across the conductor is 8 V, the resistance of the conductor is $20 \Omega$
  • D. D. When the current through the conductor is 0.2 A, the voltage across the conductor is 2 V

Answer: A

Solution: From the image, when the voltage across the conductor is 4 V, the current is 0.4 A, at this time the resistance of the conductor is $R = \frac { U } { I } = \frac { 4 } { 0.4 } \Omega = 10 \Omega$, option A is correct, B is wrong; when the voltage across the conductor is 8 V, the current on the conductor can not be determined, and can not be derived from the resistance of the resistor, option C is wrong; Similarly, when the current through the conductor is 0.2 A, the conductor is 0.2 A, the conductor ends When the current through the conductor is 0.2 A, the voltage at the ends of the conductor can not be determined, option D is wrong; Therefore, choose A.

Question 9: 10. The physical quantities defined in the following equations are not defined by the ratio method.

10. The physical quantities defined in the following equations are not defined by the ratio method.

  • A. A. $E = \frac { F } { q }$
  • B. B. $R = \rho \frac { l } { S }$
  • C. C. $R = \frac { U } { I }$
  • D. D. $C = \frac { Q } { U }$

Answer: B

Solution: A. The equation defining the field strength, using the ratio definition method, A is incorrect; B. The expression for the law of resistance, which reflects the determinants of resistance, not using the ratio definition method, B is correct; C. The deformation of Ohm's law, the defining equation of resistance, using the ratio definition method, C is incorrect; D. The defining equation of capacitance, using the ratio definition method, D error.

Question 10: 11. The unit of voltage is

11. The unit of voltage is

  • A. A. Ampere (A)
  • B. B. Ohms ( $\Omega$ )
  • C. C. Volt (V)
  • D. D. Joule (J)

Answer: C

Solution: A. The ampere (A) is the unit of current strength, so A is wrong; B. The ohm $( \Omega )$ is the unit of resistance, so B is wrong ; C. The volt (V) is the unit of voltage, so C is correct; D. Joule (J) is the unit of work and energy, so D is wrong.

Question 11: 12. Three resistors, all with resistance value $9 \Omega$, which are connected and combined in any w...

12. Three resistors, all with resistance value $9 \Omega$, which are connected and combined in any way, cannot have a total resistance of (

  • A. A. $3 \Omega$
  • B. B. $6 \Omega$
  • C. C. $15 \Omega$
  • D. D. $27 \Omega$

Answer: C

Solution: When three resistors are connected in series, the total resistance is: $3 \times 9 \Omega = 27 \Omega$; when three resistors are connected in parallel, the total resistance is: $\frac { 1 } { 3 } \times 9 \Omega = 3 \Omega$; when two resistors are connected in series in parallel with the third resistor, the total resistance is: $\frac { 18 \times 9 } { 18 + 9 } \Omega = 6 \Omega$; when two resistors are connected in parallel with the third resistor, the total resistance is: $\frac { 1 } { 2 } \times 9 \Omega + 9 \Omega = 13.5 \Omega$. The total resistance is: $\frac { 1 } { 2 } \times 9 \Omega + 9 \Omega = 13.5 \Omega$, so $15 \Omega$ is impossible; this question chooses the impossible, so choose C .

Question 12: 13. When a uniform wire with resistance $64 \Omega$ is cut into 4 equal sections and connected in pa...

13. When a uniform wire with resistance $64 \Omega$ is cut into 4 equal sections and connected in parallel, the resistance becomes

  • A. A. $32 \Omega$
  • B. B. $16 \Omega$
  • C. C. $8 \Omega$
  • D. D. $4 \Omega$

Answer: D

Solution: According to the law of resistance $$ R = \rho \frac { L } { S } $$ It can be seen that a uniform resistance wire with resistance $64 \Omega$ is truncated into 4 equal segments of equal length, so that the resistance of each segment is $16 \Omega$, and then these 4 segments of resistance are connected in parallel, then we have $$ \frac { 1 } { R _ { \text {并 } } } = \left( \frac { 1 } { 16 } + \frac { 1 } { 16 } + \frac { 1 } { 16 } + \frac { 1 } { 16 } \right) \Omega = \frac { 1 } { 4 } \Omega $$ This results in $$ R _ { \text {并 } } = 4 \Omega $$

Question 13: 14. two identical cylindrical wire A and B, now A uniformly stretched for the original twice, and th...

14. two identical cylindrical wire A and B, now A uniformly stretched for the original twice, and then connected in series in the circuit, as shown in the figure, the circuit in the C point grounded to the left end of the A for the origin, to the right for the $x$ axis of the positive direction. The image of the potential $\varphi$ in the circuit changing along the $x$ direction is ![](/images/questions/phys-dc-circuits/image-009.jpg)

  • A. A. ![](/images/questions/phys-dc-circuits/image-001.jpg)
  • B. B. ![](/images/questions/phys-dc-circuits/image-002.jpg)
  • C. C. ![](/images/questions/phys-dc-circuits/image-003.jpg)
  • D. D. ![](/images/questions/phys-dc-circuits/image-004.jpg)

Answer: D

Solution: AB. Since the direction of current in the loop is positive along the $x$ axis, the potential decreases in the positive direction along the $x$ axis, and it is known that AB is incorrect. FORMULA_5]] rod with resistance $R _ { 0 }$ per unit length, then the potential at point $A$, which is at a distance of $A$ from point $x$ is $$ \varphi = \varphi _ { 0 } - I R _ { x } = \varphi _ { 0 } - I R _ { 0 } x $$ Then the slope of the $\varphi - x$ image is $I R _ { 0 }$; the resistance per unit length on the $B$ rod is less than $R _ { 0 }$, and then the slope is less than $I R _ { 0 }$ , then image D is correct and C is incorrect.

Question 14: 15. The following statements are true about the concepts of electrical circuits, electrical energy a...

15. The following statements are true about the concepts of electrical circuits, electrical energy and the law of conservation of energy ( )

  • A. A. According to $I = \frac { U } { R }$, the current through a conductor is directly proportional to the voltage across the conductor and inversely proportional to the resistance of the conductor, so the resistance is determined by the voltage and current
  • B. B. When the power supply is short-circuited, the current is very high, the circuit voltage is zero, the internal voltage of the power supply is equal to the power supply electromotive force, and the power output of the power supply is maximum
  • C. C. Current passes through the appliance, the electrical energy consumed by the appliance is equal to the work done by the current, according to $W = I ^ { 2 } R t$, it can be seen that as long as there is a current passing through the appliance, the appliance produces heat, and all the electrical energy is converted into internal energy
  • D. D. The electromotive force of a power supply is numerically equal to the voltage between the poles of the power supply when it is not connected to a circuit, and the electromotive force of a power supply characterizes the ability of a power supply to convert other forms of energy into electrical energy.

Answer: D

Solution: A. Resistance is a property of the conductor itself, and its magnitude is determined by the material, length, cross-sectional area, and temperature of the conductor. $R = \frac { U } { I }$ is the defining formula of resistance, not the determining formula, so A is wrong; B. When the power supply is short-circuited, the external resistance $R = 0$, the circuit voltage $U = 0$, the current is $$ I = \frac { E } { r } $$ At this time the internal voltage of the power supply is equal to the supply electromotive force, and the output power of the power supply is $$ P = U I = 0 $$ Therefore, B is wrong; C. Only pure resistance circuit, the current through the appliance, electrical energy is all converted to internal energy, in the non-pure resistance circuit, $W = I ^ { 2 } R t$ calculated as electric heat, electrical energy in addition to the conversion of internal energy will be converted into other forms of energy, so C error; D. power supply electromotive force is numerically equal to the power supply is not connected to the circuit when the voltage between the poles, the electromotive force reflects the power supply to other forms of energy into electrical energy, so D is correct.

Question 15: 16. As shown in Figure A, two uniform conductor columns of the same material $a$ and $b , a$ are $l ...

16. As shown in Figure A, two uniform conductor columns of the same material $a$ and $b , a$ are $l , b$ long $l , b$ long $2 l$, and when they are connected in a circuit in series, the potential change along the $x$ axis $\varphi - x$ is shown in Figure B. FORMULA_4]] axis direction potential change $\varphi - x$ graph shown in Figure B, selected $x = 3 l$ at the potential is zero, then the ratio of the cross-sectional area of the conductor column $a , b$ is ( ) ![](/images/questions/phys-dc-circuits/image-010.jpg) A ![](/images/questions/phys-dc-circuits/image-011.jpg) B

  • A. A. $\frac { 1 } { 3 }$
  • B. B. $\frac { 1 } { 2 }$
  • C. C. $\frac { 1 } { 4 }$
  • D. D. $\frac { 2 } { 5 }$

Answer: A

Solution: From the graph, we can see that the voltage of conductor column a is 6 V and the voltage of conductor column b is 4 V. Conductor column a and conductor column b are connected in series, so the ratio of voltage is equal to the ratio of resistance, the ratio of the length of $\mathrm { a } , \mathrm {~b}$ is $1 : 2$, and the ratio of the cross-sectional area by the law of resistance $R = \frac { \rho L } { S }$ can be found as $1 : 3$. Therefore, choose A.

Question 16: 17. The total resistance of three identical resistors connected in series is $54 \Omega$, and the to...

17. The total resistance of three identical resistors connected in series is $54 \Omega$, and the total resistance of connecting them in parallel is ( )

  • A. A. $3 \Omega$
  • B. B. $6 \Omega$
  • C. C. $8 \Omega$
  • D. D. $12 \Omega$

Answer: B

Solution: Let the resistance of these three identical resistors be $R$ in series $$ R _ { \text {串 } } = 3 R = 54 \Omega $$ We have $$ R = 18 \Omega $$ Let the total resistance of connecting them in parallel be ${ } ^ { R _ { \text {并 } } }$, then $$ \frac { 1 } { R _ { \text {并 } } } = \frac { 1 } { R } + \frac { 1 } { R } + \frac { 1 } { R } $$ We have $$ R _ { \text {并 } } = \frac { R } { 3 } = 6 \Omega $$

Question 17: 18. The following statements are correct ( )

18. The following statements are correct ( )

  • A. A. Current has a magnitude and a direction, so current is vectorial
  • B. B. According to $R = \frac { U } { I }$, the higher the voltage across the conductor, the higher the resistance of the conductor
  • C. C. According to $I = \frac { U } { R }$, the current through a conductor is proportional to the voltage applied across it
  • D. D. According to $\rho = \frac { R S } { l }$, the resistivity of a conductor is directly proportional to the product of the conductor's resistance and cross-sectional area $R S$, and inversely proportional to the conductor's length $l$

Answer: C

Solution: A. The current has a magnitude and a direction, but the current is a scalar quantity and does not follow the principle of vector superposition, A error; B. The resistance is determined by the nature of the conductor itself, independent of the voltage and current, can not say that the resistance of the conductor is proportional to the voltage added to the ends of the resistance, B error; C. According to the content of Ohm's law can be known: resistance must be, through the conductor in the current is proportional to the voltage at the ends of the conductor, C is correct; D. Resistivity has nothing to do with the resistance, length, cross-sectional area of the conductor, is the electrical properties of the conductor material itself, determined by the material of the conductor, and related to temperature. The conductor of the same material, the resistivity of the conductor is unchanged, that is, the resistivity of the conductor and the resistance of the conductor and the product of cross-sectional area is independent of the length of the conductor, D error.

Question 18: 19. The figure shows the $I - U$ line of a conductor with $\alpha = 45 ^ { \circ }$, the following s...

19. The figure shows the $I - U$ line of a conductor with $\alpha = 45 ^ { \circ }$, the following statement is correct () ![](/images/questions/phys-dc-circuits/image-012.jpg)

  • A. A. The resistance of this conductor is directly proportional to the voltage across it
  • B. B. This conductor may be a semiconductor
  • C. C. $I - U$ The slope of the graph line indicates the reciprocal of the resistance, so $R = 1.0 \Omega$
  • D. D. When 6.0 V is applied across this conductor, the charge passing through the cross-section of the conductor is 3.0 C per second

Answer: D

Solution: A. As can be seen from the figure, the current increases with the increase in the voltage at its ends, so the current is proportional to the voltage at its ends, the resistance is unchanged, so A error; BC . BC. From the figure, we can see that the resistance of the conductor is $R = \frac { U } { I } = \frac { 10 } { 5 } = 2.0 \Omega$ and remains unchanged, not a semiconductor, so BC is wrong; D. When a voltage of 6.0 V is applied across the conductor, the current in the circuit is $I = \frac { U } { R } = \frac { 6.0 } { 2.0 } = 3.0 \mathrm {~A}$, and the amount of charge passing through the resistor per second is $q = I t = 3.0 \times 1 = 3.0 \mathrm { C }$; therefore, D is correct.

Question 19: 20. The following statements are correct ( )

20. The following statements are correct ( )

  • A. A. From $R = \frac { U } { I }$, we know that the resistance of a conductor is directly proportional to the voltage across it and inversely proportional to the current through it
  • B. B. The ratio $\frac { U } { I }$ reflects the nature of the conductor to impede the flow of current, i.e., resistance $R = \frac { U } { I }$
  • C. C. The higher the conductor current, the lower the resistance
  • D. D. From $I = \frac { U } { R }$, we know that the voltage across a conductor is directly proportional to the current through it

Answer: B

Solution: AC. The resistance of a conductor depends on the conductor itself, and the current depends on the voltage and resistance across the conductor; the voltage determines the current, and the current does not determine the voltage. The resistance of a conductor depends on the conductor itself and has nothing to do with $U$ or $I$, so AC is wrong; B. The ratio $\frac { U } { I }$ reflects the resistance of a conductor to current and is defined as resistance, so B is correct; D. From the relationship between current and voltage, we know that voltage is the cause of current, so the correct statement is that "the current through a conductor is directly proportional to the voltage applied to its ends", and the cause and effect relationship can not be reversed, so D is wrong.

Question 20: 21. Neglecting the effect of temperature on resistance, the following statements are false () ##...

21. Neglecting the effect of temperature on resistance, the following statements are false () ## Area is inversely proportional

  • A. A. According to $R = U / I$, when the current through the conductor remains constant and the voltage applied across the resistor is twice the original, the resistance of the conductor also becomes twice the original
  • B. B. According to $R = U / I$, the resistance of the conductor remains unchanged, although the voltage applied across the resistor is twice the original voltage
  • C. C. According to $R = \frac { \rho L } { S }$, the resistance of a conductor is proportional to the resistivity of the conductor and the length of the conductor, and to the cross-section of the conductor
  • D. D. The resistivity of a conductor is independent of the conductor's resistance $R$, cross-sectional area $S$, and conductor length $L$.

Answer: A

Solution: Resistance is the nature of the conductor itself, and the voltage at the ends of the conductor has nothing to do; therefore, A is wrong; B is correct; according to $R = \rho \frac { L } { S }$ know, the resistance of the conductor with the conductor's resistivity and the length of the conductor is directly proportional to the conductor, and the conductor cross-sectional area inversely proportional to the conductor; therefore, C is correct; the conductor's resistivity is a material itself to determine the physical quantities, and the length of the conductor L, the cross sectional area of the conductor, the resistance R are irrelevant; therefore, D is correct; this question is wrong, so the choice of A is wrong. resistance R are irrelevant, so D is correct; this question is wrong, so choose A. [Eyes on] this question to know $R = \frac { U } { I }$ is the definition of resistance, $R = \rho \frac { L } { S }$ is the determination of resistance, resistivity $\rho$ by the conductor material, $\rho$ is a physical quantity determined by the material itself, the conductor's resistivity is the length L, cross-sectional area S, the conductor's resistance R are unrelated. The resistivity $\rho$ is determined by the conductor material itself and is independent of the length L, cross-sectional area S, and resistance R of the conductor.

Question 21: 22. With respect to the understanding of Ohm's law, one of the following statements is correct

22. With respect to the understanding of Ohm's law, one of the following statements is correct

  • A. A. Ohm's law applies to all conducting substances
  • B. B. From $R = \frac { U } { I }$, the resistance of a conductor is directly proportional to the voltage across it and inversely proportional to the current through it
  • C. C. From $I = \frac { U } { R }$, the current through a resistor is proportional to the voltage across it and inversely proportional to its resistance
  • D. D. For a purely resistive element, the ratio of the voltage across it to the current through it must remain constant

Answer: C

Solution: A. Ohm's law applies to purely resistive circuits or electrolyte conductivity, not to all conducting substances; therefore, A error; B. conductor resistance by the conductor material, length, cross-sectional area, independent of voltage and current, so B error; C. Ohm's law is: the current through the conductor is proportional to the voltage across it, and its resistance is inversely proportional to, so C is correct; D. for the resistance of the pure resistance components, the voltage at its ends and the ratio of the current through it is unchanged, equal to the resistance, so D is wrong; [Eyes] know the factors affecting the size of the resistance, and know that the resistance of the conductor and the conductor voltage and current through the key to solving this problem, Ohm's law is only a method of calculating resistance.

Question 22: 24. A metal rod of length $L$ and cross-sectional area $S$ has resistivity $\rho$, the number of fre...

24. A metal rod of length $L$ and cross-sectional area $S$ has resistivity $\rho$, the number of free electrons per unit volume in the rod is $n$, the mass of the electrons is $m$, and the charge is $e$. FORMULA_4]] and the charge is $e$. When a constant voltage is applied to both ends of the bar, a current is generated in the bar and the free electrons move directionally at an average rate of $v$ , then the potential difference between the ends of the metal bar is

  • A. A. pnevL
  • B. B. $\frac { m v ^ { 2 } S n } { e }$
  • C. C. $\frac { m v ^ { 2 } } { 2 e }$
  • D. D. $\frac { \rho e v } { S }$

Answer: A

Solution: According to the law of resistance, the resistance of the metal bar is found to be $$ R = \rho \frac { L } { S } $$ The current in the metal rod can be expressed as $$ I = n e S v $$ Then the voltage applied across the metal rod is $$ U = I R $$ The potential difference between the two ends of the metal rod can be obtained by association as $$ U = \rho n e v L $$

Question 23: 25. With different materials made of two identical shape and size of the resistor A, B, their $U - I...

25. With different materials made of two identical shape and size of the resistor A, B, their $U - I$ image shown in the figure. If the resistivity of $\mathrm { A } , \mathrm {~B}$ is $\rho _ { \mathrm { A } } , \rho _ { \mathrm { B } }$ respectively, the following statement is correct ![](/images/questions/phys-dc-circuits/image-013.jpg)

  • A. A. $\rho _ { \mathrm { A } } > \rho _ { \mathrm { B } }$
  • B. B. $\rho _ { \mathrm { A } } < \rho _ { \mathrm { B } }$
  • C. C. The overall $U - I$ image of A and B in parallel may be C
  • D. D. The overall $U - I$ image of A and B in series may be $C$

Answer: A

Solution: The slope of the $\mathrm { AB } . U - I$ image is the resistance, which is shown by the title graph $$ R _ { \mathrm { A } } > R _ { \mathrm { B } } $$ By the law of resistance $R = \rho \frac { l } { s }$, the resistance of two resistors of exactly the same shape and size is directly proportional to the resistivity, thus $$ \rho _ { \mathrm { A } } > \rho _ { \mathrm { B } } $$ A is correct and B is incorrect; C. The resistance of A and B in parallel is less than the resistance of either branch, therefore $$ R _ { \mathrm { A } } > R _ { \mathrm { B } } > R _ { \text {并 } } $$ The $U - I$ image of the whole after A and B are connected in parallel is not C. C is wrong; D. The resistance of A and B in series is greater than that of any one of the resistors, therefore $$ R _ { \text {中 } } > R _ { \mathrm { A } } > R _ { \mathrm { B } } $$ The $U - I$ image of A and B in series is not C. D is wrong.

Question 24: 26. In the circuit shown in the figure, point O is grounded, and when the original disconnected s is...

26. In the circuit shown in the figure, point O is grounded, and when the original disconnected s is closed, the potentials at points A and B will be ( ) [IMAGE_0]]

  • A. A. both are elevated
  • B. B. both lower
  • C. C. Point A is elevated, point B is lowered
  • D. D. Point A decreases, point B increases

Answer: A

Solution: After the switch s closes, the resistance between OB decreases, the voltage between two points of OB $\mathrm { U } _ { \mathrm { OB } }$ decreases by the principle of series voltage divider, $U _ { O B } = \varphi _ { o } - \varphi _ { B } = - \varphi _ { B }$, so the potential of point B increases, and similarly the voltage between two points of AO increases, and the potential of point A rises, A is right;

Question 25: 27. two thick and thin, different materials, metal rods A, B connected together after access to the ...

27. two thick and thin, different materials, metal rods A, B connected together after access to the circuit, known as the ratio of the length of the two rods $L _ { A } L _ { B } = 21$, resistivity $\rho _ { A } \rho _ { B } = 12$, as shown in the figure, then the following statements are correct () $\xrightarrow { I } = \square A$ B

  • A. A. The voltage at the ends of the A rods is less than the voltage at the ends of the B rods.
  • B. B. The strength of the current through the two rods is not equal
  • C. C. Equal resistance of both rods
  • D. D. The thermal power produced by the current flowing through the two rods is not equal

Answer: C

Solution: According to $R = \rho \frac { L } { S }$, we can know that the ratio of the resistance of the metal rods $\mathrm { A } , \mathrm {~B}$ is ${ } _ { 1 : 1 }$, and they are connected in series in the circuit, and the intensity of the current through the two rods is equal, and according to $U = I R$, we can know that the voltage of the two ends of the A rod is equal to the voltage of the two ends of the B rod. According to $P = I ^ { 2 } R$, it can be known that the thermal power produced by the current flowing through the two rods is equal, so C is correct, and A, B and D are wrong;

Question 26: 28. The following statements about the resistance of a conductor are correct

28. The following statements about the resistance of a conductor are correct

  • A. A. The resistance of a conductor is directly proportional to the voltage across the conductor
  • B. B. The resistance of a conductor is inversely proportional to the strength of the current in the conductor
  • C. C. The resistance of a conductor is determined by the strength of the current in the conductor and the voltage across the terminals of the conductor
  • D. D. The resistance of a conductor is determined by the material, length and cross-sectional area of the conductor

Answer: D

Solution: The resistance of a conductor is determined by the conductor itself, independent of the voltage across the conductor and the strength of the current in the conductor, option ABC is incorrect; the resistance of a conductor is determined by the material, length and cross-sectional area of the conductor, option D is correct.

Question 27: 29. The image of $I - U$ for the resistor $R _ { 1 } , R _ { 2 }$ is shown in Figure ![](/images/que...

29. The image of $I - U$ for the resistor $R _ { 1 } , R _ { 2 }$ is shown in Figure ![](/images/questions/phys-dc-circuits/image-015.jpg)

  • A. A. $R _ { 1 } > R _ { 2 }$
  • B. B. $R _ { 1 } < R _ { 2 }$
  • C. C. The voltage increases and the resistance value of ${ } ^ { R _ { 2 } }$ becomes larger.
  • D. D. The voltage increases and the resistance value of ${ } ^ { R _ { 2 } }$ becomes smaller.

Answer: B

Solution: AB . According to Ohm's law $R = \frac { U } { I }$, the slope of the $I - U$ image is equal to the reciprocal of the resistance, and there are $$ R _ { 1 } < R _ { 2 } $$ Therefore, A is wrong and B is correct; CD. Since ${ } ^ { R _ { 2 } }$ corresponds to $I - U _ { \text {the slope of the graph remains unchanged, so the voltage increases,} } { } ^ { R _ { 2 } }$, the resistance value of $I - U _ { \text {the slope of the graph remains unchanged, so the voltage increases,} } { } ^ { R _ { 2 } }$ remains unchanged, so CD is wrong. Therefore, choose B.

Question 28: The current $I$ of a small bulb varies with the applied voltage $U$ as shown in the figure, $P$ is a...

The current $I$ of a small bulb varies with the applied voltage $U$ as shown in the figure, $P$ is a point on the graph line, $P N$ is the tangent to the line, $P Q$ is the vertical line of the $U$ axis, and $P M$ is the tangent to the line. FORMULA_4]] is the vertical line of the $U$ axis, and $P M$ is the vertical line of the $I$ axis. The following statement is false ( ) ![](/images/questions/phys-dc-circuits/image-016.jpg)

  • A. A. As the applied voltage increases, the resistance of the small bulb increases
  • B. B. Corresponding to point $P$, the resistance of the small bulb is $R = \frac { U _ { 1 } } { I _ { 2 } }$
  • C. C. In a circuit where the voltage across the bulb L is $U _ { 1 }$, the voltage across the resistor $R$ in series with the bulb is ${ } _ { 1 } R$.
  • D. D. Corresponding to the point $P$, the power of the small bulb is the area enclosed by the rectangle $P Q O M$ in the figure

Answer: C

Solution: A. According to Ohm's law $R = \frac { U } { I }$, we can know $I - U$ that the slope of the line connecting the point and the origin is equal to the reciprocal of the resistance, and from mathematical knowledge, we can know that with the increase of the applied voltage, the applied current increases, and the resistance of the small bulb increases, so A is correct; B. Corresponding to the point $I - U$, the resistance of the small bulb is the same as the voltage. _3]] point, the resistance of the small bulb is B. Corresponding to , the resistance of the bulb is $$ R = \frac { U _ { 1 } } { I _ { 2 } } $$ Therefore, B is correct; C. When the voltage across bulb L in the circuit is $U _ { 1 }$, the voltage across resistor $R$ is ${ } ^ { I _ { 2 } R }$, so C is wrong; D. By the constant current power formula $P = U I$, promotion can be known, corresponding to the $P$ point, the power of the small bulb for the figure of the rectangular area surrounded by the PQOM, so D is correct; This question selects the wrong item, so choose C.

Question 29: 32. In the investigation of the quantitative relationship between the conductor resistance and its i...

32. In the investigation of the quantitative relationship between the conductor resistance and its influencing factors, a student according to the circuit shown in the figure for the experimental study, in which the conductor $a$ and $b$ is just a different length, $a$ and $c$ is just a different thickness, $a$ and $d$ is just a different thickness. FORMULA_3]] are only different in thickness, $a$ and $d$ are only different in material, and the following statements about the experiment are correct ( ) ![](/images/questions/phys-dc-circuits/image-017.jpg)

  • A. A. This circuit lacks an ammeter, so it is not possible to investigate quantitative relationships
  • B. B. $a$ Compared to $b$, the longer the conductor, the smaller the voltage indication.
  • C. C. $a$ Compared to $c$, the thicker the conductor, the larger the voltage indication.
  • D. D. $a$ Compared to $d$, the smaller the voltage indication, the better the conductivity of that material

Answer: D

Solution: A. The circuit is a series circuit, the current through each conductor is equal, and the quantitative relationship between the resistance of each conductor can be obtained from the voltage representation, A is wrong; B. The conductors $a$ and $b$ are only different in length, and according to the law of resistance, the longer the length, the greater the resistance, and according to Ohm's law, the greater the voltage; C. Compared with $a$ and $c$, according to the law of resistance, the thicker the conductor is, the lower the resistance is and the lower the voltage is, C is wrong; D. Compared with $a$ and $d$, the smaller the voltage is, the smaller the resistance is, and according to the law of resistance, the smaller the resistivity is, the better the conductivity of the material is, D is correct.

Question 30: 33. In the rainstorm, if the high-voltage line support tower leakage, when people close to the suppo...

33. In the rainstorm, if the high-voltage line support tower leakage, when people close to the support tower near the wetlands, very easy to electrocution accidents, access to information that: when the current through the human torso to reach more than 0.1 A will be life-threatening. As shown in the figure, if a person from the bottom of the support tower for the horizontal distance of 10 m, the distance between the two feet for the 0.5 m, each foot of the resistance of $300 \Omega$, the torso part of the resistance of $900 \Omega$, per meter of wetland resistance of $120 \Omega$, the current flowing through the human torso is 0.1 A. Then, the human torso will be electrocuted when the current through the human body reaches 0.1 A or more. The current is 0.1 A. Then ( ) ![](/images/questions/phys-dc-circuits/image-018.jpg)

  • A. A. The total body resistance connected to the circuit is $1200 \Omega$
  • B. B. 150 V between the two pins
  • C. C. The current flowing through the wetland is 2 A
  • D. D. Reducing the distance between your feet is more dangerous.

Answer: B

Solution: A. The total resistance of the human body connected to the circuit is the total resistance of the two feet in series with the torso so there is $1500 \Omega$, then $A$ is wrong; B. The voltage between the two feet is $$ U = I R _ { \curlywedge } = 0.1 \times 1500 = 150 \mathrm {~V} $$ So B is correct ; C. The current flowing through the wetland is $$ I _ { \text {地 } } = \frac { U } { R _ { \text {地 } } } = \frac { 150 } { 0.5 \times 120 } = 2.5 \mathrm {~A} $$ So C is wrong ; D.When the distance between the two feet is reduced, the voltage between the two feet decreases, and the current through the body decreases, then the danger is reduced, so D is wrong ;

Question 31: 34. As shown in the figure, $R _ { 1 } , R _ { 2 }$ is a metal conductor of the same material, the s...

34. As shown in the figure, $R _ { 1 } , R _ { 2 }$ is a metal conductor of the same material, the same thickness, the surface of the square, the ratio of the lengths of the sides of the square is $2 : 1$, the direction of the current through the two conductors as shown in the figure, do not take into account the effect of the temperature on the resistivity, then the two conductors and $_ { 2 }$ ( ) ![](/images/questions/phys-dc-circuits/image-019.jpg)

  • A. A. The ratio of resistivity is $2 : 1$
  • B. B. The ratio of resistance is $4 : 1$
  • C. C. Connected in series in a circuit, the ratio of the voltage across the terminals is $1 : 1$
  • D. D. Connected in series in a circuit, the ratio of the rates of directional movement of free electrons is $2 : 1$

Answer: C

Solution: A. The resistivity is determined by the metal itself, then the ratio of the resistivity of two conductors $R _ { 1 }$ and $R _ { 2 }$ is $1 : 1$, so A is wrong; B. Let the length of the side of a square be $L$, and the thickness be [[]]. INLINE_FORMULA_8]], and according to the law of resistance, we can see that $$ R = \rho \frac { L } { S } = \rho \frac { L } { L d } = \frac { \rho } { d } $$ The ratio of the resistance of the two conductors is $$ R _ { 1 } : R _ { 2 } = 1 : 1 $$ Therefore, B is incorrect; C. The two conductors are connected in series in the circuit, and the currents through them are equal. According to Ohm's law, the ratio of the voltages across the two resistors is $1 : 1$, so C is correct; D. Since the two conductors are connected in series, the currents passing through them are equal, according to the microscopic expression for current $$ I = n e S v $$ It is known that the ratio of the rate of directional movement of free electrons in ${ } ^ { R }$ and ${ } ^ { R }$ is $$ v _ { 1 } : v _ { 2 } = S _ { 2 } : S _ { 1 } = 1 : 2 $$ Therefore, D is wrong.

Question 32: 35. As shown in the figure, if the $x$ axis represents time and the $y$ axis represents velocity, th...

35. As shown in the figure, if the $x$ axis represents time and the $y$ axis represents velocity, then the area under the line represents the displacement, and the slope of the line $A B$ represents the magnitude of the object's acceleration at that moment. If the $x$ and $y$ axes are used to represent other physical quantities, the relationship between the corresponding physical quantities in a certain situation can be reflected. The following statement is correct ( ) ![](/images/questions/phys-dc-circuits/image-020.jpg)

  • A. A. If the direction of the electric field is parallel to the $x$ axis, the $x$ axis represents the position, and the $y$ axis represents the electric potential, the slope of the straight line $A B$ represents the magnitude of the electric field strength at the corresponding position
  • B. B. If the $x$ axis represents time and the $y$ axis represents the magnetic flux through a tightly wound solenoid, then the slope of the straight line $A B$ represents the magnitude of the electromotive force generated by the solenoid
  • C. C. If the $x$ axis represents the current flowing through a resistor and the $y$ axis represents the voltage across the resistor, then the area under the graph line represents the thermal power of the resistor
  • D. D. If the $x$ axis represents time and the $y$ axis represents the amount of charge passing through the cross-sectional area of the conductor, then the area under the line of the graph represents the work done by the current in this time period

Answer: A

Solution: A. If the direction of the electric field is parallel to the $x$ axis, the $x$ axis indicates the position, the $y$ axis indicates the electric potential, and the slope of the $\varphi ^ { - } x$ image indicates the strength of the field. FORMULA_4]] indicates the magnitude of the electric field at the corresponding position, so A is correct; B. If the $x$ axis represents time and the $y$ axis represents the magnetic flux passing through the tightly wound solenoid, the slope of the $\Phi - t$ image represents the rate of change of the magnetic flux, so B is wrong; C. If the $x$ axis represents the current flowing through a resistor, and the $y$ axis represents the voltage across the resistor, then the product of the voltage at a point on the image and the current at that point in the $U - I$ image represents the thermal power, so C is wrong; D. If the $x$ axis represents time and the $y$ axis represents the amount of charge passing through the cross-sectional area of a conductor, the area under the graph line is meaningless, so D is wrong. The area under the graph line has no meaning, so D is incorrect.

Question 33: 36. After a voltage $U$ is applied across a conductor of resistance $R$, a graph of the amount of ch...

36. After a voltage $U$ is applied across a conductor of resistance $R$, a graph of the amount of charge $q$ passing through the cross-section of the conductor versus the time of energization $t$ is shown. The magnitude of the slope of this graph line is $k$, then the following relationship is correct ( ) ![](/images/questions/phys-dc-circuits/image-021.jpg)

  • A. A. $k = \frac { R } { U }$
  • B. B. $t = k q$
  • C. C. $R = \frac { U } { k }$
  • D. D. $k = R$

Answer: C

Solution: According to the definition of current, we can get $$ I = \frac { q } { t } $$ From the magnitude of the slope of the graph line $k$, we get $$ I = k $$ From Ohm's law we have $$ I = \frac { U } { R } $$ Therefore $$ k = \frac { q } { t } = \frac { U } { R } $$ Therefore, C is correct and ABD is incorrect.

Question 34: 37. In the $U - I$ diagram shown in the figure, the line $a$ is the relationship between the voltage...

37. In the $U - I$ diagram shown in the figure, the line $a$ is the relationship between the voltage and current at the circuit end of a power supply, and the line $b$ is the relationship between the voltage and current of a resistor $R$. Now this power supply is directly connected to the resistor $R$ to form a closed circuit, from the figure () ![](/images/questions/phys-dc-circuits/image-022.jpg)

  • A. A. The resistance value of this resistor is $2.0 \Omega$
  • B. B. This power supply has an electromotive force of 6.0 V and an internal resistance of $0.5 \Omega$
  • C. C. The circuit voltage of this power supply is 4.0 V and the output power is 4.0 W
  • D. D. By forming a closed loop with this power supply with a resistor larger than the $R$ resistance, the output power of the power supply may increase

Answer: C

Solution: A. From the graph $b$, we can see that the external resistance $$ R = \frac { U } { I } = \frac { 4 } { 1 } \Omega = 4 \Omega $$ Therefore, A is incorrect. B. From the graph $a$, we can know that the electric potential of the power supply $E = 6.0 \mathrm {~V}$, the short-circuit current $I _ { \text {短 } } = 3.0 \mathrm {~A}$, and the internal resistance of the power supply are $I _ { \text {短 } } = 3.0 \mathrm {~A}$. $$ r = \frac { E } { I _ { \text {短 } } } = \frac { 6 } { 3 } \Omega = 2 \Omega $$ Therefore, B is wrong. C. By the coordinates of the intersection of the two images, the roadside voltage is 4.0 V, the dry circuit current is 1.0 A, the power output of the power supply is $$ P _ { \text {出 } } = U I = 4.0 \times 1.0 \mathrm {~W} = 4.0 \mathrm {~W} $$ Therefore, C is correct. D. The internal resistance of the power supply is $r = 2 \Omega$ and the resistance is $R = 4 \Omega$, because when the external resistance $R$ is equal to the internal resistance $r$, the power supply has the maximum output power. FORMULA_11]] resistance is larger than that of $R$, the power output of the power supply will be reduced, option D is wrong.

Question 35: 38. As shown in the figure for an electrical component of the volt-ampere characteristic curve, the ...

38. As shown in the figure for an electrical component of the volt-ampere characteristic curve, the dotted line for the curve on the $P$ point of the tangent line. When the current through the component is 0.4 A, the resistance value of the component is ( ) ![](/images/questions/phys-dc-circuits/image-023.jpg)

  • A. A. $250 \Omega$
  • B. B. $125 \Omega$
  • C. C. $100 \Omega$
  • D. D. $62.5 \Omega$

Answer: B

Solution: From the figure, when the current is 0.4 A, the voltage is 50 V. Then, by Ohm's law, the resistance value $R = \frac { U } { I } = \frac { 50 } { 0.4 } \Omega = 125 \Omega$ is $R = \frac { U } { I } = \frac { 50 } { 0.4 } \Omega = 125 \Omega$, so B is correct and ACD is wrong.

Question 36: 39. In the figure $a , b$, the straight lines represent the volt-ampere characteristic curves of two...

39. In the figure $a , b$, the straight lines represent the volt-ampere characteristic curves of two resistance wires of the same length and uniform thickness made of the same material. Regarding these two resistance wires, the following judgment is correct ( ) ![](/images/questions/phys-dc-circuits/image-024.jpg)

  • A. A. Resistance wire $a$ Thinner
  • B. B. Resistance wire $b$ Thinner
  • C. C. If the resistance wires $a , b$ are connected in series to the circuit, the voltage across $b$ is larger
  • D. D. If the resistance wires $a , b$ are connected in parallel to the circuit, the current through $a$ is larger

Answer: A

Solution: AB . From the volt-ampere characteristic curve of the resistance wire, we know that $$ R _ { a } > R _ { b } $$ When the material and length are the same, then by the law of resistance $$ R _ { a } = \rho \frac { L } { S _ { a } } , \quad R _ { b } = \rho \frac { L } { S _ { b } } $$ can be obtained $$ S _ { a } < S _ { b } $$ That is, the resistance wire $a$ is thinner and the resistance wire $b$ is thicker, A is correct and B is wrong; C. The resistance wire $a , b$ is connected in series, and their currents are equal, and the voltage at the ends of the resistor with the larger resistance is larger, i.e., the resistance wire $a$ is thinner. $$ U _ { a } > U _ { b } $$ C Error ; D. Resistance wire $a , b$ parallel connection they are equal voltage, the resistance of the larger current is smaller, that is $$ I _ { a } < I _ { b } $$ D error.

Question 37: 40. As shown in the figure, three resistors $R _ { 1 } , R _ { 2 } , R _ { 3 }$ have the same resist...

40. As shown in the figure, three resistors $R _ { 1 } , R _ { 2 } , R _ { 3 }$ have the same resistance value and the maximum voltage allowed across the resistors is 5 V , 5 V, 4 V, then the maximum voltage allowed in this circuit is ( ) ![](/images/questions/phys-dc-circuits/image-025.jpg) High School Physics Assignment, October 30, 2025

  • A. A. 15 V
  • B. B. 12 V
  • C. C. 9 V
  • D. D. 7.5 V

Answer: D

Solution: Since the three resistors have the same resistance value and the maximum voltage allowed by $R _ { 1 } , R _ { 2 }$ is the same, combined with the way the circuit is connected, it can be seen that when the voltage of the circuit is at its maximum, the voltage at the two ends of $R _ { 1 }$ is $5 \mathrm {~V} , R _ { 2 } , R _ { 3 }$ is in parallel with the voltage being equal, and the total current of the two is equal to the current flowing through $R _ { 1 }$, then the total current of both is equal to the current flowing through the $5 \mathrm {~V} , R _ { 2 } , R _ { 3 }$. INLINE_FORMULA_6]] in parallel, and the current of the $$ \frac { 5 } { R } = 2 \frac { U } { R } $$ ## Solution. $$ U = 2.5 \mathrm {~V} $$ The maximum voltage allowed in the circuit is $$ U _ { \mathrm { m } } = U + 5 \mathrm {~V} = 7.5 \mathrm {~V} $$
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DC Circuits

直流电路

37 Practice Questions

Practice with Chinese questions to prepare for the CSCA exam. You can toggle translations while practicing.

Topic Overview

DC circuits is a fundamental module in the Physics exam, focusing on the relationship between current, resistance and power at constant voltage. The questions often combine I-U images to analyze resistance properties, series-parallel calculations, and nonlinear components (e.g., diodes). Mastery of Ohm's law and image interpretation is the key to solving the questions.

Questions:37

Key Points

  • 1Ohm's law and its application to series-parallel circuits
  • 2Analysis of linear and nonlinear characteristics of resistors by I-U images
  • 3Calculation of electrical power and parameters at rated operating conditions
  • 4Voltammetric characterization of nonlinear components such as diodes

Study Tips

More practice is recommended in extracting resistances from I-U images, comparing slopes, and distinguishing the operating characteristics of linear versus nonlinear components.

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