** Mesh analysis or loop analysis** involves the application of Kirchhoff’s voltage law to a circuit. KVL provides linear equations which are used to obtain current in branches.

## 5 Steps to Apply Mesh Analysis

- Assign a clockwise current direction to all loops in a network
- Label the loops and indicate the voltage polarity
- Apply Kirchhoff’s voltage law to the loops (Any resistor common to two loops will have two voltage drops)
- Application of KVL will yield simultaneous equations that should be solved
- Branch currents that are common to a branch are algebraically determined by combining the loop currents

## An Example

Let’s solve an example to better understand this.

Consider the circuit below:

Apply Kirchhoff’s voltage law in the left loop:

V(1) = V(R1) + V(R2)

5 V = 5 Ω * I_{1} + 15 Ω ( I_{1} – I_{2})

5 V = I_{1} (5 + 15) – 15 I_{2}

20 I_{1} – 15 I_{2} = 5* … Eqn(1)*

Apply Kirchhoff’s voltage law in right loop:

V(R2) + V(R3) + V(2) = 0

15 Ω ( I_{2} – I_{1}) + 10 Ω I_{2} + 12 V = 0

15 I_{1} – 25 I_{2} = 12* … Eqn(2)*

Solving these two equations we have:

I_{1} = -0.2 A

I_{2} = -0.6 A

Negative symbol in both equations indicate that actual current is flowing in opposite direction.