Question

# A cell of emf E is connected to a resistance R1 for time t and the amount of heat generated in it is H. If the resistance R1 is replaced by another resistance R2 and is connected to the cell for the same time t, the amount of heat generated in R2 is 4H. Then internal resistance of the cell is:

A
2R1+R22
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B
R1R2×2R2R1R22R1
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C
R1R2×R22R12R2R1
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D
R1R2×R2R1R2+R1
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Solution

## The correct option is C √R1R2×√R2−2√R12√R2−√R1Heat generated is given as, H=I2R×tAccording to given condition:⇒I21R1×t=H and I22R2×t=4H⇒E2(R1+r)2R1×t=H and E2(R2+r)2R2×t=4H⇒R2(R2+r)2=4R1(R1+r)2⇒√(R2+r)(R1+r)=2√R1(R2+r)On solving, r=√R1R2×√R2−2√R12√R2−√R1

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