What is Kirchhoff’s Voltage Law

Starting at any node in a circuit, we form a loop by traversing through elements (open-circuits included!) and returning to the starting node, never encountering any other node more than once.

 Figure 1 : For example, the paths fabef and fdcef are loops:


 Figure 2 : whereas the paths becba and fde are not


Kirchhoff’s  Voltage  Law  (KVL)  is  essentially  the  law  of  conservation  of energy. If voltages across elements traversed from – to + are positive in sense, and voltages across elements that are traversed from + to – are negative in sense (or vice versa), then KVL can be stated as follows:

KVL defined as

KVL: Around any loop in a circuit, the voltages algebraically sum to zero.

If there are n elements in the loop then, in symbols, KVL is:


KVL can also be stated as: In traversing a loop, the sum of the voltage rises equals the sum of the voltage drops.

Example 1

In the circuit shown in Figure 1, we select a traversal from – to + to be positive in sense. Then KVL around the loop abcefa gives:

– v1 – v2  + v3  – v8  + v6  = 0

and around loop bcdeb, we have:

– v2  – 3 – v4  + v7  = 0

In this last loop, one of the elements traversed (the element between nodes b and e) is an open-circuit; however, KVL holds regardless of the nature of the elements in the circuit.

Example 2

We want to find the current i, in the one-loop circuit shown below:


The polarities of v1 , v2 , v3 and the direction of i were chosen arbitrarily (the polarities of the 10 V and 34 V sources are given). Applying KVL we get:

10 – v1 – 34 – v2  + v3  = 0


v1 + v2  – v3  = -24

From Ohm’s Law:

v1  = 2i

v2  = 4i

v3  = -6i

Substituting these into the previous equation yields:

(2i) + (4i) – (- 6i) = -24

2i + 4i + 6i = -24

12i = -24

i = -2 A

Having solved for i, we now find that:

v1  = 2i = 2(- 2) = -4 V

v2  = 4i = 4(- 2) = -8 V

v3  = -6i = (- 6)(- 2) = 12 V

Share With Your Friends

Don't Miss Our Updates
Be the first to get exclusive content straight to your email.
We promise not to spam you. You can unsubscribe at any time.
Invalid email address

Leave a Comment

What is Kirchhoff’s Voltage Law

Send this to a friend