Mesh Analysis [Loop Analysis]

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

1. Assign a clockwise current direction to all loops in a network
2. Label the loops and indicate the voltage polarity
3. Apply Kirchhoff’s voltage law to the loops (Any resistor common to two loops will have two voltage drops)
4. Application of KVL will yield simultaneous equations that should be solved
5. 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 * I₁ + 15 Ω ( I₁ – I₂)

5 V = I₁ (5 + 15) – 15 I₂

20 I₁ – 15 I₂ = 5 … Eqn(1)

Apply Kirchhoff’s voltage law in right loop:

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

15 Ω ( I₂ – I₁) + 10 Ω I₂ + 12 V = 0

15 I₁ – 25 I₂ = 12 … Eqn(2)

Solving these two equations we have:

I₁ = -0.2 A

I₂ = -0.6 A

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