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Kirchhoff's Voltage Law

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Kirchhoff's Voltage Law — KVL

The beginner version is:

What the source gives, the circuit must account for.

Another way to think of this

If you climb 12 feet and return to exactly where you started, all the rises and drops during the trip must add back to zero net change. Voltage around a closed electrical loop behaves similarly.

What is really happening?

Kirchhoff's Voltage Law says that the algebraic sum of voltage changes around any closed loop is zero:

ΣV = 0

We may call a source a voltage rise and loads voltage drops.

Worked example

A 12 V source supplies two series loads. One drops 4 V:

12 - 4 - V₂ = 0

V₂ = 8 V

Kirchhoff's two laws together

KCL handles what happens at junctions. KVL handles what happens around loops. Together with Ohm's law, they can solve a very large range of ordinary DC resistor networks.

Try these yourself

A 12 V source has one 4 V drop. What must the other series drop be? 4 V 6 V 8 V 16 V

The drops around the loop must add to the source: 4 V + 8 V = 12 V.

What does Kirchhoff's Voltage Law say around a complete loop? Voltage rises and drops balance Current is always 1 A Resistance becomes zero Every component has the same voltage

The algebraic sum of all voltage rises and drops around a closed loop is zero.

A 24 V source supplies series drops of 6 V, 8 V, and one unknown. What is the unknown drop? 8 V 10 V 14 V 18 V

24 - 6 - 8 = 10 V.

A little deeper

In more advanced electromagnetic situations, a changing magnetic field can induce an electromotive force around a loop. For our beginning steady DC circuits, the simple KVL form above is exactly the tool we need.

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