Question

In the following circuit, $18\Omega$ resistor develops $2J$ due to current flowing through it. The power
developed across $10\Omega$ resistance is

• A. $\frac{4}{5}W$
• B. $125W$
• C. $10W$
• D. $25W$

Answer 1

The correct option is C $10W$

Two $12\Omega$ resistance and three $9\Omega$ resistance is connected in parallel. So the circuit can be redrawn as:

Now, the current will be divided at the junction in inverse ratio of resistance since the voltage is
same in parallel.
$\frac{i_1}{i_2}=\frac{9}{18}=\frac{1}{2}$
And $i=i_1+i_2$
$\frac{i}{i_1}=1+\frac{i_2}{i_1}=1+2=3$
We know that,
$P=i^{2}R$
$\Rightarrow \frac{P_{10\Omega }}{P18\Omega }$$={\left(\frac{i}{i_1}\right)}^2\times \frac{10}{18}$$\Rightarrow P_{10\Omega }=10W$
Hence, option $\left(b\right)$ is correct