Question

A cell of emf $\varepsilon$ and internal resistance 'r' is connected to an external variable resistance R. The total thermal power generated in the circuit is maximum, if R is equal to:

• A. r
• B. zero
• C. 2 r
• D. r/2

Answer 1

Answer: (A)

r

Answer 2

The current in the circuit is

$i = \frac{\varepsilon}{r + R}$

and the power dissipated in the resistor $R$ is given by

$P = i^2R = \frac{\varepsilon^2R}{(r+R)^2}$.

For maximum power, differentiate $P$ with respect to $R$ and equate to zero:

$\frac{dP}{dR}=0 \quad \Rightarrow \quad R = r$.