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
Options:
A .  r21r2
B .  r22r1
C .  12(r1+r2)
D .  √r1r2
Answer: Option D : D In the first case the current in the circuit is l1=Er1+r Q1=l2r1t=(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+2rr2+r2)=r2(r21+2rr1+r2) r2(r1−r2)=r1r2(r1−r2) r=√r1r2
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