Question

In the circuit shown in figure, for what value of $\text{R}$ will the power consumed by this resistance will be maximum.

• A. $40\Omega$
• B. $\frac{20}{3}\Omega$
• C. $\frac{10}{7}\Omega$
• D. $30\Omega$

Answer 1

The correct option is B $\frac{20}{3}\Omega$

We need to reduce this circuit to a battery and a single resistor.

$6\Omega$ and $4\Omega$ resistance are in series


Now , we can assume a cell of $emf=0$ $\text{V}$ is connected with $20\Omega$ resistance.


So this $0\text{V}$ and $20\text{V}$battery are in parallel combination.

Their equiavlent resisatnce, $r_{eq}=\frac{20\times 10}{20+10}=\frac{20}{3}\Omega$

Let their equiavlent emf be $V$


This can be further reduced to,



Using maximum power transfer theorem. We can say that $R$ should be equal to $\frac{20}{3}\Omega$ for maximum power transfer.