Kirchhoff's Voltage Law
The sum of voltages around any closed loop is zero.
Formula
Variables
Example
Around any loop, the battery’s voltage equals the sum of the voltage drops.
How it works
Kirchhoff's Voltage Law says that if you start at any point in a circuit and travel all the way around one closed loop, the total rise in electric potential must equal the total drop, so the net change is zero. This follows from conservation of energy: a charge that returns to where it started cannot end up with extra or missing energy. In practice, every battery, resistor, and other component contributes a positive or negative voltage depending on the direction you traverse it.
When to use it
Use this when analysing loop circuits, especially ones with batteries and resistors in series or mesh circuits with multiple branches. It is one of the main equations for finding unknown currents or voltages in DC circuit problems.
Worked example, step by step
A loop contains a 12 V battery and three resistors with voltage drops of 3 V, 4 V, and 5 V. Write Kirchhoff's Voltage Law: sum V = 0 Substitute the signed voltages around the loop: +12 - 3 - 4 - 5 = 0 Check the arithmetic: 12 - 3 - 4 - 5 = 0 So the loop is balanced, and the battery's 12 V supply is exactly used up across the three resistors.
Common mistakes to avoid
- forgetting to assign signs to voltage rises and drops
- mixing up voltage and current when writing the loop equation
- including components that are not actually in the closed path
Did You Know?
Around any loop, the voltage gains and drops must cancel — energy can't be created in a circuit.
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