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Ammeter

The circuit s...

Question

The circuit shown in Figure contains three resistors $R_{1} = 100 Ω$ , $R_{2} = 50 Ω$ , and $R_{3} = 20 Ω$ and cells of emfs $E_{1} = 2 V$ and $E_{2}$ . The ammeter indicates a current of 50 mA. Determine the currents in the resistors and the emf of the second cell. The internal resistance of the ammeter and of the cells should be neglected.

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Solution

Given : $E_{1} = 2$ V $R_{1} = 100 Ω$ $R_{2} = 50 Ω$ $R_{3} = 20 Ω$
Kirchhoff'l loop law in ABCDA : $- E_{1} + (I + 0.05) R_{1} + I R_{2} = 0$
$∴$ $- 2 + (I + 0.05) (100) + I (50) = 0$ $⟹ I = - 0.02$ A

Kirchhoff'l loop law in BGEFB : $- E_{2} + (0.05) R_{3} + (I + 0.05) R_{1} = 0$
$∴$ $- E_{2} + (0.05) (20) + (- 0.02 + 0.05) (100) = 0$ $⟹ E_{2} = 4$ V
Hence current flowing through $R_{1}$ , $I_{1} = 0.05 - 0.02 = 0.03$ A $= 30$ mA towards right

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