Question

Figure (32-E10) shows a part of an electric circuit. The potentials at the points a, b and c are 30 V, 12 V and 2 V respectively. Find the currents through the three resistors.
Figure 32-E10

Answer 1

The current passing through the three resistors is 0.6 A.

Explanation:

At point o, the potential be X volts. From the figure,  

Vo = XSo, i1 = Va - Vo10Va = 30V, i1 = 30-X10

Likewise, i2 = Vo - Vb20 = X-1220

And i3 = X-230

We observe from kirchoff’s junction law that

i1 = i2 + i3

⇒ 30-X10 = X-1220+X-230

⇒30-X=X-122+X-23

⇒180-6X = 5X-40

⇒X = 22011 = 20 V

So, through the three resistors, the passing current is:  

i1 = 30-2010 = 1Ai2 = 0.6 A.