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Question

A current of 2 A flows through a 2 Ω resistance when connected across a battery. The same battery supplies a current of 0.5 A when connected across a 9 Ω resistor. The internal resistance of the battery is

A
0.5 Ω
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B
13 Ω
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C
15 Ω
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D
1 Ω
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Solution

The correct option is B 13 Ω
Let the internal resistance of the battery be r. Then, the current flowing through the circuit is given by
I=ER+r
case 1: 2=E2+r(i)
case 2: 0.5=E9+r(ii)
Equating E from (i) and (ii)
4+2r=4.5+0.5r
1.5r=0.5
r=13 Ω

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