BeginnerTopic 11 of 106Electrical Engineering

Kirchhoff's voltage law

Voltages around any closed loop sum to zero because energy is conserved.

In depth

Around any closed loop the algebraic sum of voltage rises and drops is zero: ΣV=0. It expresses energy conservation. Loop equations or mesh analysis rely on it.

Key points

  • Follow the loop direction consistently
  • Resistor drop is IR in direction of current
  • Works with AC phasors too
Example

12 V source with two resistors: 12 = V₁+V₂.

Why it matters

This law is the basis of loop analysis and tells you that voltage drops must add up around any closed path.

Where this is used

  • Checking the voltage drop across a battery and a chain of resistors.
  • Writing loop equations for a multi-battery circuit.
  • Verifying an unexpected reading on a test board.

Frequently asked questions

What is Kirchhoff's voltage law?

Voltages around any closed loop sum to zero because energy is conserved.

Why is it important to understand kirchhoff's voltage law?

This law is the basis of loop analysis and tells you that voltage drops must add up around any closed path.

How do I choose the sign of each voltage in a loop?

Pick a loop direction, then treat a voltage as positive if you meet it going from minus to plus. Apply the same rule consistently.

Does KVL hold in circuits with changing magnetic fields?

Not in the simple lumped form. Induced EMFs in loops must be added as sources, which is why the physical field needs to be considered.

How is Kirchhoff's voltage law used in practice?

Typical applications include checking the voltage drop across a battery and a chain of resistors, writing loop equations for a multi-battery circuit and verifying an unexpected reading on a test board.

What should I learn before Kirchhoff's voltage law?

Study "Kirchhoff's current law" first (topic 10 of 106 in Electrical Engineering). It covers the groundwork this topic builds on.

What are the key points of Kirchhoff's voltage law?

Follow the loop direction consistently. Resistor drop is IR in direction of current. Works with AC phasors too.

Can you give an example of Kirchhoff's voltage law?

12 V source with two resistors: 12 = V₁+V₂.

What comes after Kirchhoff's voltage law?

The next topic is "Voltage and current dividers", which builds directly on this one.

How difficult is Kirchhoff's voltage law?

It is classed as Beginner in Electrical Engineering (topic 11 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.

Learning path

Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.

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