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Question

A battery of emf E and internal resistance r is connected to a resistor of resistance r1 and Q joules of heat is produced in a certain time t. When the same battery is connected to another resistor of resistance r2 the same quantity of heat is produced in the same time t the value of r is


Solution

The correct option is C

In the first case the current in the circuit is 
l1=Er1+r
Q1=l2 r1 t=(Er1+r)2 ×r1× t
In the second case 
Q2=(Er1+r)2 ×r2× t
equating above equations we get
r1(r1+r)2=r2(r2+r)2
r1(r2+r)2=r2(r1+r)2
r1(r22+2 r r2+r2)=r2(r21+2r r1+r2)
r2(r1r2)=r1r2(r1r2)
r=r1r2

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