Question

In the following circuit, $5\Omega$ resistor develops $45J/s$ due to current flowing through it. The power developed per second across $12\Omega$ resistor is

• A. $16W$
• B. $192W$
• C. $36W$
• D. $64W$

Answer 1

The correct option is B $192W$

Let the current flowing through upper branch be $i_2$ and lower branch be $i_1$ and the total current flowing through the circuit be $i$. Now, since the voltage is same in parallel then,
$i_1(9\Omega +6\Omega )=i_2\left(15\Omega \right)$
$\frac{i_1}{i_1}=\frac{15}{3}=3\dots \left(i\right)$
Also $\frac{H}{t}=i^{2}R$
$45=(i_1{)}^2\times 5$
$i_1=3A$
From equation (i)
$i_2=1A$
So $i=i_1+i_2=4A$

Now power developed across $12\Omega$ resistance is
$P=i^{2}R$$=(4{)}^2\times 12=192W$
Hence, option $\left(b\right)$ is correct.