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A battery of 80 V with an internal resistance of 2 Ω is to be charged from 200 V mains. Find the value of the series resistance for charging current o

Question

A battery of 80 V with an internal resistance of 2 Ω is to be charged from 200 V mains. Find the value of the series resistance for charging current of 5 A.

20 Ω

24 Ω

22 Ω

18 Ω

Solution

Correct option is C

$\text{Where } V = \text{Source voltage} = 200 \, \text{V}, \, E = \text{Battery} = 80 \, \text{V}, \, R = \text{Unknown Series Resistance} \, \text{In this given circuit,}\\V = 200 \, \text{V}, \, E = 80 \, \text{V}, \, \text{Internal resistance } (r) = 2 \, \Omega\\\text{As per KVL, } \\V - I R - I r - E = 0; \, I = \text{current in given circuit} = 5 \, \text{A}\\200 - I \times R - I \times 2 - 80 = 0\\5R = 200 - 80 - 10 = 110\\R = \frac{110}{5} = 22 \, \Omega$