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Kirchhoff's voltage law
Intermediate
Voltages around a loop sum to zero.
ΣV = 0Around any closed loop the sum of EMFs equals the sum of potential drops: ΣV = 0, from energy conservation.
A 12 V battery with two resistors: V₁ + V₂ = 12.
Be careful with signs: drops along the current direction.
In more detail
Kirchhoff's voltage law states that the sum of voltage changes around any closed loop in a circuit is zero. It follows from the conservation of energy.
Real-world uses
- Solving circuits with several loops and sources.
- Checking voltage drops in power networks.
- Engineers analysing a loop of components use Kirchhoff's voltage law to find the unknown voltage across one part.
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Frequently asked questions
What if the loop includes a battery?
The battery's EMF is treated as a voltage rise, and resistors as drops.
Is it always valid?
For circuits where magnetic fields are negligible, yes.
Which way do I go round the loop?
Either way works, as long as you add rises and subtract drops consistently for each component.
Related topics in Current Electricity & Circuits
EMF and internal resistance · Cells in series and parallel · Kirchhoff's current law · Wheatstone bridge · Meter bridge · Potentiometer