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Q.

A cell of constant e.m.f. is first connected to a resistance R1 and then connected to a resistance R2. If power delivered in both cases is same, then the internal resistance of the cell is

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a

R1R2

b

R1R2

c

R1−R22

d

R1+R22

answer is A.

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Detailed Solution

Power dissipated =i2R =  ER+r2R∴   ER1+r2R1 =  ER2+r2R2⇒  R1 R22 +  r2 +  2R2r = R2 R12+r2 +  2R1r⇒ R22R1 + R1r2 + 2R1R2r= R12R2 + R2r2 + 2R1R2r⇒  R1 − R2r2 =  R1 − R2R1R2 ⇒  r= R1R2
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