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

Answer: 2

From circuit, $\frac{1}{R}=\frac{1}{3}+\frac{1}{6}=\frac{2+1}{6}=\frac{3}{6}\Omega$
$\Rightarrow R_1=2\Omega$

$R_2=(R_2+R_2)\parallel R_4=2\Omega$
The internal resistance of battery $=1\Omega$
So, the equivalent resistance of circuit $=2\Omega +1\Omega =3\Omega$
The current in the battery,
$I=\frac{V}{R}=\frac{4.5}{3}=1.5A$
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,
$P=I^2\times R$
$={\left(\frac{1}{2}\right)}^2\times 3$
$=\frac{1}{4}\times 3$
$=0.75W$