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Question

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

A
1/3Ω
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B
1/4Ω
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C
1Ω
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D
0.5Ω
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Solution

The correct option is B 1/3Ω
Given,
I1=2A,I2=0.5A
R1=2Ω,R2=9Ω
Supplied voltage is same.
To find,
Internal Resistance of battery,r=?
E=V+Ir
E=IR+Ir
E=I(R+r)
I=E(R+r)
E1=2(2+r) and E2=0.5(9+r)
As the supplied voltage is same,
So, E1=E22(2+r)=0.5(9+r)
20.5=9+r2+r
4=9+r2+r
4(2+r)=(9+r)
8+4r=9+r
4rr=98
3r=1
r=13Ω
Therefore, Internal Resistance of battery is 13Ω


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