Current Electricity - Result Question 79
84. A battery of $10 V$ and internal resistance $0.5 \Omega$ is connected across a variable resistance $R$. The value of $R$ for which the power delivered is maximum is equal to
[2001, 1992]
(a) $0.25 \Omega$
(b) $0.5 \Omega$
(c) $1.0 \Omega$
(d) $2.0 \Omega$
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Answer:
Correct Answer: 84. (b)
Solution:
- (b) Power is maximum when $r=R, R=r=0.5 \Omega$.
If a cell of internal resistance $r$ and emf $E$ is connected to an external resistance of radius $R$, then current given by cell, $I=\frac{E}{R+r}$
Power dissipated in external resistance (load) $P=V I=(I R) I=I^{2} R$
$\Rightarrow P=(\frac{E}{R+r})^{2} R$
when $R=r$
Power, $P=\frac{E^{2}}{4 r}$ (Maximum)
