电压diànyā

Core Concept

Voltage (电压), also called potential difference (电势差), is the energy delivered per unit charge as it moves between two points. It is what drives current — the electrical analogue of a pressure difference pushing water through a pipe.

The crucial point students miss: voltage is always measured between two points. "The voltage at point A" is meaningless without a reference. Current flows through an element; voltage exists across it.

Definition

$U = \frac{W}{Q}$

• $W$ — work done moving the charge, in joules
• $Q$ — charge moved, in coulombs
• SI unit: volt ($\mathrm{V}$); $1\ \mathrm{V} = 1\ \mathrm{J/C}$

Ohm's Law Form

$U = IR$

This is the form used in almost every CSCA circuit question, particularly 计算电阻串联或并联时的电压 — one of the highest-frequency physics knowledge points.

How Voltage Divides

In series, voltage divides in proportion to resistance:

$\frac{U_1}{U_2} = \frac{R_1}{R_2}, \qquad U_1 + U_2 = U_{\text{total}}$

The larger resistor takes the larger share. The voltage divider formula follows directly:

$U_1 = U_{\text{total}} \cdot \frac{R_1}{R_1 + R_2}$

In parallel, every branch has the same voltage — the source voltage — regardless of branch resistance.

EMF vs Terminal Voltage

A real source has internal resistance $r$, so the voltage at its terminals is less than its electromotive force $\varepsilon$:

$U = \varepsilon - Ir$

The larger the current drawn, the more voltage is lost internally. This is why a battery's terminal voltage sags under heavy load.

CSCA Practice Problems

💡 Note: These problems follow the CSCA exam syllabus and Chinese standardized test formats.

Example 1: Basic (Difficulty ★★☆☆☆)

Three identical $4\ \Omega$ resistors are connected in parallel across a $12\ \mathrm{V}$ source. The voltage across each resistor is:

Options:

• A. $4\ \mathrm{V}$
• B. $6\ \mathrm{V}$
• C. $12\ \mathrm{V}$
• D. $36\ \mathrm{V}$

Detailed Solution:

Parallel branches all share the same voltage, which is the source voltage. So each resistor has $12\ \mathrm{V}$ across it, regardless of how many branches there are.

Option A is the trap for dividing the source by three — that is what happens in series, not parallel. Reciting "parallel shares voltage" prevents it.

Answer: C

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Example 2: Intermediate (Difficulty ★★★☆☆)

A $9\ \mathrm{V}$ battery with internal resistance $1\ \Omega$ is connected to a $2\ \Omega$ external resistor. Find the terminal voltage.

Options:

• A. $3\ \mathrm{V}$
• B. $6\ \mathrm{V}$
• C. $9\ \mathrm{V}$
• D. $18\ \mathrm{V}$

Detailed Solution:

1. The internal and external resistances are in series with the same current: $I = \frac{\varepsilon}{R + r} = \frac{9}{2 + 1} = 3\ \mathrm{A}$

2. Terminal voltage is the EMF minus the internal drop: $U = \varepsilon - Ir = 9 - (3)(1) = 6\ \mathrm{V}$

3. Cross-check by looking at the external resistor instead: $U = IR = 3 \times 2 = 6\ \mathrm{V} \ ✓$

Answer: B

Common Mistakes

❌ Mistake 1: Dividing the source voltage among parallel branches

Parallel branches all get the full source voltage. Only series elements share it out.

❌ Mistake 2: Talking about voltage "at" a point

Voltage is a difference between two points. Say "across the resistor", not "at the resistor".

❌ Mistake 3: Treating terminal voltage as equal to EMF

They are equal only when no current flows. Under load, $U = \varepsilon - Ir < \varepsilon$.

❌ Mistake 4: Giving the larger voltage share to the smaller resistor

In series, $U \propto R$. The bigger resistance takes the bigger drop.

Study Tips

1. ✅ Repeat "current through, voltage across" — it fixes most wording confusion
2. ✅ Learn the divider formula $U_1 = U\frac{R_1}{R_1+R_2}$ — it skips finding $I$
3. ✅ Check that series drops sum to the source every time
4. ✅ Watch for internal resistance whenever a question mentions a battery's EMF
5. ✅ In parallel, stop calculating — the branch voltage is simply the source voltage

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💡 Exam Tip: 计算电阻串联或并联时的电压 is among the most-repeated CSCA physics knowledge points. The question is nearly always testing one thing: whether you know which quantity is shared in which configuration.