Question

A battery with internal resistance of $4 \,\Omega$ is connected to a circuit consisting three resistances, $R, \,2 R$ and $4R$ (see following figure). If the power generated in the circuit is highest, then the magnitude of $R$ must be

• A. $4 \Omega$
• B. $7 \Omega$
• C. $10 \Omega$
• D. $14 \Omega$

Answer 1

Answer: (B)

For maximum power output, external resistance value must be equals to internal resistance of source. In given circuit, $R, \,2R$ and $4R$ resistance are in parallel and their equivalent resistance is $R_{ eq }$
So, $\frac{1}{R_{ eq }}=\frac{1}{R}+\frac{1}{2 R}+\frac{1}{4 R}$ or $R_{ eq }=\frac{4 R}{7}$
For maximum power,
$R_{ eq }=r$
$\Rightarrow \,\frac{4 R}{7}=4 \,\Omega$
$ R=7\, \Omega$