The EMF of the batteries with internal resistance is connected in the circuit shown below. The equivalent EMF and internal resistance of the circuit between terminal 'AB' are equal to ______.

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Question

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AAI ATC Junior Executive 21 Feb 2023 Shift 1 Official Paper

Answer 1

Concept:

In this circuit all cells are in parallel and in parallel equivalent internal resistance is given as

And equivalent EMF is given as

\(\epsilon_{eq}=r_{eq}(\frac{\epsilon_1}{r_1}+\frac{\epsilon_2}{r_2}+\frac{\epsilon_3}{r_3})\)

Explanation:

\(\frac{1}{r_{eq}}=\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}\)

\(\frac{1}{r_{eq}}=\frac{1}{0.1}+\frac{1}{0.2}+\frac{1}{0.2}\)

\(r_{eq}=\frac{1}{20}=0.05\Omega\)

\(\epsilon_{eq}=r_{eq}(\frac{\epsilon_1}{r_1}+\frac{\epsilon_2}{r_2}+\frac{\epsilon_3}{r_3})\)

\(\epsilon_{eq}=0.05(\frac{2}{0.1}-\frac{4}{0.2}+\frac{6}{0.2})\)

\(\epsilon_{eq}=\frac{5\times30}{100}=1.5V\)

Hence, the correct answer is Option-4.

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