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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 1/3ΩGiven,I1=2A,I2=0.5AR1=2Ω,R2=9ΩSupplied voltage is same.To find,Internal Resistance of battery,r=?E=V+I⋅rE=I⋅R+I⋅rE=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=E2⇒2⋅(2+r)=0.5⋅(9+r)⇒20.5=9+r2+r⇒4=9+r2+r⇒4⋅(2+r)=(9+r)⇒8+4r=9+r⇒4r−r=9−8⇒3r=1⇒r=13ΩTherefore, Internal Resistance of battery is 13Ω

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