Question

In the circuit shown in Fig. E26.28, find (a) the current in each branch and (b) the potential difference V_ab of point a relative to point b.

Answer 1

(a)
Let current in top, middile & bottom branch be i1,i2 & i3 respectively !!

Using Kirchoff Voltage and Current Law,
2.0 * i1 + 10.0 * i3 + 3.0 * i1= 10.0
5.0 * i1 + 10.0 * i3 = 10.0
i1 + 2.0 * i3 = 2.0 ---------1

2.0 * i1 + 1.0 * i2 + 5.0 + 4.0 * i2 +  3.0 * i1= 10.0
5.0 * i1 + 5.0 * i2 = 5.0
i1 + i2 = 1.0 -----------2

i1 = i2 + i3 -------3

Solving the above eq,
i1 = 0.8 A
i2 = 0.2 A
i3 = 0.6 A

Current in top branch, i1 = 0.8 A
Current in middle branch, i2 = 0.2 A
Current in bottom branch, i3 = 0.6 A

(b)
Vab = 4.0 * i2 + 3.0 * i1
Vab = 4.0 * 0.2 + 3.0 * 0.8
Vab = 3.2 V