Question

If the power dissipated (in $watt$ ) in $3\,\Omega$ resistance in the following circuit is $\frac{1 . 5}{x}W$ then find $x$ .

Answer 1

From circuit, $\frac{1}{R}=\frac{1}{3}+\frac{1}{6}=\frac{2 + 1}{6}=\frac{3}{6}\,\Omega$
$\Rightarrow R_{1}=2\,\Omega$

$R_{2}=\left(\right. R_{2} + R_{2} \left.\right)\parallel R_{4}=2\,\Omega$
The internal resistance of battery $=1\,\Omega$
So, the equivalent resistance of circuit $=2\,\Omega+1\,\Omega=3\,\Omega$
The current in the battery,
$I=\frac{V}{R}=\frac{4 .5}{3}=1.5\,A$
Current in $3\Omega$ is, $\frac{1 .5}{2}\times \frac{2}{3}A=\frac{1}{2}A$
The power dissipated in $3\,\Omega$ resistance,
$P=I^{2}\times R$
$=\left(\frac{1}{2}\right)^{2}\times 3$
$=\frac{1}{4}\times 3$
$=0.75 \, W$