Use mesh analysis to obtain i1, i2 and i3 in the circuit in Fig. 3.84.Figure 3.84

The mesh currents are labeled to the circuit is shown in Figure 2.

Figure 2

Apply Kirchhoff's voltage law, the algebraic sum of all voltages around a closed path (or loop) is zero.

For mesh 1, Kirchhoff's voltage law gives,

…… (1)

For mesh 2, Kirchhoff's voltage law gives,

…… (2)

Multiply equation (1) by 3 and equation (2) by 5 and add both equations.

Substitute the value of in equation (1).

Determine the branch current, .

Therefore, the current is.

Determine the branch current, .

Therefore, the current is.

Determine the branch current, .

Therefore, the value of current is.