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
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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:
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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