We have to calculate (a) the current through each source of emf in the circuit shown in the figure. (b) We have to calculate . We may assume that , , and .

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In the circuit shown above currents have been indicated in the different branches, and its multi-loops can be fixed by affixing labels to corners and intersections.

Data of the problem are

,

and .

(b)

We will solve this problem by applying Kirchoff’s laws to different loops in the circuit.

Applying Kirchoff’s laws to loops dabcd and afeba, we write the following two equations:

Solving equations and , we find

Substituting the data given above, we find

The current flowing through is

As we are interested in the magnitudes of currents and not their directions, the currents flowing through , and are 668 mA, 85.7 mA and 582.3 mA, respectively.

(a)

From the section ba of the circuit, we calculate .

We have