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Phasor Diagrams in AC Circuits

Three identic...

Question

Three identical batteries each emf 4 V and zero of negligible internal resistance are connected as shown in figure below. The potential difference between the poiints A and G ( $V_{A} - V_{G}$ )

A

4 V

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B

- 4 V

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C

8 V

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D

- 8 V

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Solution

The correct option is B $- 4 V$
Current in ABCDA loop : $I_{1} = \frac{4}{2 + 2} = 1 A$
Current in EFGHE loop : $I_{2} = \frac{4}{3 + 3} = 2 / 3 A$
Applying KVL A to G, $V_{A} + 2 I_{1} + 4 - 3 I_{2} = V_{G}$
or $V_{A} - V_{G} = 3 I_{2} - 2 I_{1} - 4 = 3 (2 / 3) - 2 - 4 = - 4$ V

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