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Question

The e.m.f. of a cell is ε and its internal resistance is r. Its terminals are connected to a resistance R. The potential difference between the terminals is 1.6 V for R=4Ω and 1.8 V for R=9Ω. Then,

A
ε=1V,r=1Ω
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B
ε=2V,r=1Ω
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C
ε=2V,r=2Ω
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D
ε=2.5V,r=0.5Ω
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Solution

The correct option is B ε=2V,r=1Ω
Case 1:
V=IR
I=Er+4
V=EIR
1.6=E(Er+4)R
On rearranging,
Er+4=0.4(1)
Case 2:
V=IR
I=Er+9
V=EIR
1.8=E(Er+9)R
On rearranging,
Er+9=0.2(2)
Equating (1) and (2), we get
r+9r+4=2
On solving above equation,
r=1 Ω
Substituting this value in (1),
E1+4=0.4
E=2 V

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