he power dissipated in the circuit shown in the figure is $30\,W$. The value of $R$ is ............. $\Omega$
AIPMT 2012, Medium
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The equivalent resistance of the given circuit is
$R_{\mathrm{eq}}=\frac{5 \,R}{5+R}$
Power dissipated in the given circuit is
${P=\frac{V^{2}}{R_{\mathrm{eq}}} \text { or } 30=\frac{(10)^{2}}{\left(\frac{5\, R}{5+R}\right)}} $
${150\, R=100(5+R)}$
${150\, R=500+100\, R \quad \text { or } 50\, R=500} $
${R=\frac{500}{50}=10\, \Omega}$
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