Question

In the circuit shown, the heat produced in $5\Omega$ resistance due to current through it is $50J{s}^{-1}$ . Then, the heat generated per second in the $2\Omega$ resistance is

• A. $5J{s}^{-1}$
• B. $4J{s}^{-1}$
• C. $9J{s}^{-1}$
• D. $10J{s}^{-1}$

Answer 1

Answer: (A)

Power is given as, $P=50J{s}^{-1}$
$P=Vi\Rightarrow P=i^{2}R$

$\Rightarrow$ $i_2^2=\frac{P}{R}=\frac{50}{5}=10A^2$
$V=i^2{R}_{\left(5\Omega \right)}$
$=\sqrt{10}\times 5=\sqrt{250}V$
and $2\Omega$ and $8\Omega$ are in series.
So, the required resistance $=2\Omega +8\Omega =10\Omega$
$i_1=\frac{V}{R_{\left(10\Omega \right)}}$
$i_1=\frac{\sqrt{250}}{10}A$
The heat generated per second in $2\Omega$ is given by,
$P=V{i}_1$
$=i_1^2\times R$
$={\left(\frac{\sqrt{250}}{10}\right)}^2\times 2$
$=\frac{250}{100}\times 2=\frac{25}{10}\times 2=\frac{25}{5}=5J{s}^{-1}$