Question

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

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

Answer 1

Answer: (A)

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

$\Rightarrow $ $i_{2}^{2}=\frac{P}{R}=\frac{50}{5}=10 \, A^{2}$
$V=i^{2}R_{\left(5 \, \Omega \right)}$
$= \, \sqrt{10}\times 5= \, \sqrt{250} \, V$
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,
$P=Vi_{1}$
$=i_{1}^{2}\times R$
$=\left(\frac{\sqrt{250}}{10}\right)^{2}\times 2$
$=\frac{250}{100}\times 2=\frac{25}{10}\times 2=\frac{25}{5}=5Js^{- 1}$