Kirchhoff's voltage law
Around any closed loop the emfs equal the drops: ΣE = ΣIR. A 10 V cell with 2, 3 and 5 Ω in series drives 1 A, and the drops 2 V + 3 V + 5 V add back to 10 V.
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Equivalent resistance10 Ωbetween A and B
Current1 Afrom the cell
Power10 WP = VI
| R | I | V | Power | |
|---|---|---|---|---|
| R₁ | 2 Ω | 1 A | 2 V | 2 W |
| R₂ | 3 Ω | 1 A | 3 V | 3 W |
| R₃ | 5 Ω | 1 A | 5 V | 5 W |
Step by step
- All in series: Req = 2 + 3 + 5 = 10 Ω
- Current from the cell: I = V / Req = 10 / 10 = 1 A
- Drops in series: R₁: 1 × 2 = 2 V, R₂: 1 × 3 = 3 V, R₃: 1 × 5 = 5 V.
- Power: P = EI = 10 × 1 = 10 W.
Why it works
- The potential at a point has one value. Go round a loop and you come back to the same point, so the total change is zero.
- Crossing a cell from - to + raises the potential by E. Crossing it from + to - lowers it by E.
- Crossing a resistor along the current lowers the potential by IR. Against the current it rises by IR.
- Add the changes round the loop and set the sum to zero: ΣE = ΣIR.
- This is the conservation of energy for a charge taken once round the loop.
Kirchhoff's voltage law: quick answers
What is Kirchhoff's voltage law?
In any closed loop, the sum of the emfs equals the sum of the IR drops. Also called the loop rule or the second law.
Which conservation law is it based on?
The conservation of energy. A charge that goes round a loop and returns gains as much energy from the cells as it loses in the resistors.
What sign does a resistor get?
Minus IR when you cross it in the direction of the current, plus IR against it. A cell is plus E from its - to its + terminal.