Question

A battery with internal resistance of $4\Omega$ is connected to a circuit consisting three resistances, $R,2R$ 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, $\frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{2R}+\frac{1}{4R}$ or $R_{eq}=\frac{4R}{7}$
For maximum power,
$R_{eq}=r$
$\Rightarrow \frac{4R}{7}=4\Omega$
$R=7\Omega$