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Kirchoff's Loop Law

A circuit is ...

Question

A circuit is shown in the figure. The ratio of current $\frac{i_{1}}{i_{2}}$ is

A

2

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B

8

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C

0.5

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D

4

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Solution

The correct option is C 8
In the given circuit applying Kirchhoff's Law in loop ABCFA, we get,
$- 8 (4 i_{2}) + 16 = 0$
$- 32 i_{2} + 16 = 0$
$i_{2} = \frac{1}{2} A$
Also, for loop CDEFC, we get,
$4 (i_{1} - 4 i_{2}) + 8 - 16 = 0$
$i_{1} = 4 A$
$∴ \frac{i_{1}}{i_{2}} = 8$

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