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Kirchhoff's voltage law (KVL) examples

Kirchhoff's voltage law (KVL) says that around any closed loop, the voltage rises add up to the voltage drops. A battery lifts charge up; resistors, LEDs and switches let it back down. One lap ends where it started, so the totals must match. Here it is at work on four real loops.

ΣVrises = ΣVdrops

Example 1: the drop you can't measure

A 9 V battery, a resistor and a red LED in one loop. The LED drops about 2.0 V. What does the resistor drop?

9 = 2.0 + VR, so VR = 7 V

That's the rule behind every LED resistor calculation: the resistor gets what's left.

Example 2: solve the current

Now two resistors and the LED: 9 V, R1 = 330 Ω, R2 = 1 kΩ, and the LED's 2 V. The resistors share 9 − 2 = 7 V, and they're in series, so:

I = 7 V over 330 Ω + 1000 Ω ≈ 5.3 mA

Then each drop is I × R: R1 takes about 1.7 V and R2 about 5.3 V. Check with KVL: 1.7 + 5.3 + 2.0 = 9 V. The bigger resistor always takes the bigger share.

Live experiment

Share out the 9 V

A 9 V battery, R1 (330 Ω), R2, a switch and Pip, a red LED, in one loop. One bar is the battery's rise, the other stacks the drops. Change R2 from 100 Ω to 2.2 kΩ and the shares move, but they always add to 9 V. Then open the switch.

Try it yourself: free lesson

“Kirchhoff's voltage law” is lesson 5 of 7 in Junction City, Electronics World 2. Free with an account. Lessons unlock in order, so you’ll do the 11 before it first.

Example 3: the open switch

Open a switch in that loop and the current stops. Every resistor now drops 0 V, and the LED drops nothing either. KVL still holds, so the full 9 V sits across the switch's gap. A voltmeter across an open switch reads the supply, which is why an open switch on mains is still dangerous inside.

Example 4: two batteries facing each other

A charger is a source pushing against a battery. A 6 V supply charges a 4.8 V pack of four rechargeable cells through 120 Ω. The two face each other, so the resistor gets the difference:

VR = 6 − 4.8 = 1.2 V
I = 1.2 V over 120 Ω = 10 mA

The current flows into the pack's + terminal, which is what charging means. As the pack fills, its voltage rises towards about 5.6 V, the difference shrinks, and the current tails off.

KVL is conservation of energy: a charge gains energy crossing the battery and gives exactly that much away round the loop.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“Kirchhoff's voltage law” is lesson 5 of 7 in Junction City, Electronics World 2. Free with an account. Lessons unlock in order, so you’ll do the 11 before it first.

Or start from the very first lesson, no account needed

Work it out

Practice questions

Three quick questions from the lessons. Pick an answer to check it.

  1. Question 1 of 3Around any closed loop, the voltages…
    Show the answer

    Answer: add up so that the rises equal the drops. That's Kirchhoff's voltage law. The energy charge gains in the battery is all given up in the drops, so you end where you started.

    • Why not “are the full battery voltage across each part”? With current flowing, the parts share the battery's voltage. Only their drops added together make the full voltage.
    • Why not “depend on how long the wires are”? Ordinary wires drop almost nothing, whatever their length. The rule holds for any closed loop, long or short.
  2. Question 2 of 3You chain four cells but the load reads 3 V. Most likely…
    Show the answer

    Answer: One cell is the wrong way round. Three forward and one back is 1.5 + 1.5 − 1.5 + 1.5 = 3 V. Four cells chained the right way read 6.

    • Why not “The load is too small”? A different load changes the current, not the sum of the cells' pushes. Four cells facing the same way still add to about 6 V.
    • Why not “The wires are too long”? Wires drop very little. Losing exactly half the voltage points to a cell facing the wrong way.
    • Why not “One cell is missing”? With a cell missing, three would read 4.5 V. Exactly 3 V is one cell pushing back: 1.5 + 1.5 + 1.5 − 1.5.
  3. Question 3 of 3Two 1.5 V cells, but one is flipped round. How much push do they give?
    Show the answer

    Answer: 0 V. The flipped cell pushes the other way, so the two pushes cancel. 1.5 − 1.5 = 0 V, and nothing flows.

    • Why not “1.5 V”? 1.5 V would mean the flipped cell did nothing. It pushes back just as hard, cancelling the other.
    • Why not “3 V”? 3 V is what two cells give facing the same way. Flipped, one subtracts: 1.5 − 1.5 = 0 V.
Keep practising: free lesson

“Kirchhoff's voltage law” is lesson 5 of 7 in Junction City, Electronics World 2. Free with an account. Lessons unlock in order, so you’ll do the 11 before it first.

Questions people ask

What does Kirchhoff's voltage law say?

Around any closed loop, the voltage rises add up to the voltage drops. Put another way, the voltages round a loop sum to zero when you count rises as plus and drops as minus. It's conservation of energy for charge.

Why is there voltage across an open switch?

With the switch open no current flows, so every resistor drops I × R = 0 V. The loop's drops must still add up to the supply, so the whole supply appears across the gap. That's why a switched-off light switch is still live inside.

What sign do I use for each voltage in KVL?

Pick a direction round the loop and stick to it. Crossing a battery from − to + is a rise; crossing a part in the direction the current flows is a drop. Get the direction of an unknown current wrong and it just comes out negative.

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