If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Class 12 Physics (India)

Course: Class 12 Physics (India)>Unit 3

Lesson 8: Kirchhoff's loop rule

Kirchhoff's loop rule review

Review the key terms and skills related to Kirchhoff's loop rule, including how to determine the electric potential difference across a component.

Key terms

TermMeaning
LoopClosed circuit that starts and ends at the same point.

Kirchhoff’s loop rule

Kirchhoff’s loop rule states that the sum of all the electric potential differences around a loop is zero. It is also sometimes called Kirchhoff’s voltage law or Kirchhoff’s second law. This means that the energy supplied by the battery is used up by all the other components in a loop, since energy can’t enter or leave a closed circuit. The rule is an application of the conservation of energy in terms of electric potential difference, delta, V.
Mathematically, this can be written as:
\Sigma, delta, V, equals, 0

How to determine the electric potential difference across a circuit component

For example, we can use Kirchhoff’s loop rule to find the unknown electric potential difference across a resistor (Figure 1).
Figure 1: A circuit with two resistors, R, start subscript, 1, end subscript and R, start subscript, 2, end subscript. V, start subscript, 2, end subscript is unknown.
Let’s pick our starting point at the battery and go around the loop until we are back to the same point.
The electric potential increase over the battery is \epsilon. Over R, start subscript, 1, end subscript there is an electric potential decrease of V, start subscript, 1, end subscript. We do not know the electric potential decrease V, start subscript, 2, end subscript over R, start subscript, 2, end subscript.
Now we can use the loop rule to solve for V, start subscript, 2, end subscript in terms of V, start subscript, 1, end subscript and \epsilon:
\begin{aligned}\Sigma \Delta V &= 0 \\\\ -V_1 - V_2 + \epsilon &= 0 \\\\ V_2&=\epsilon-V_1\end{aligned}

For deeper explanations, see our video on Kirchhoff's loop rule (or voltage law).
To check your understanding and work toward mastering these concepts, check out our exercises:

Want to join the conversation?

• I am trying to master Kirchoff's loop rule, but I don't understand how you setup the loop.

A loop is a closed circuit where you start and end at the same point. But I don't understand... sometimes they use an left loop, sometimes a right loop, sometimes and outer loop, ect.

Can I please get clarification on how to use Kirchoff's voltage/loop law?

Thanks! :)
• You can use any loop you want. You just have to make sure that your signs are right and you do the correct operations. Once you take a loop, you need to identify your voltage sources and your resistors. The sum of the voltage drops across the resistors must equal to the total voltage that the current starts out with. Hope this helps!
• how do i master Kirchhoff's rule?
ways to simplify the whole concept.
• Practise is the only key. Start from khan academy's practise sheets, they are the of the lowest level, designed to introduce concept and then increase your level slowly from various problems from different books or other sources.
• In some of the practice questions with multiple loops there was a voltage rise around loops without an additional voltage source. How is it possible that the current would flow against the given flow from the one voltage source??