In the figure shown the power generated in $y$ is maximum when $y = 5\,\Omega$ . Then $R$ is .............. $\Omega$
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The current $i$ is$:$
$i=\frac{10}{2+R+y}$
Power, $P=i^{2} R$
$P=\frac{100}{(2+R+y)^{2}} y$
The power will be maximum where $d P / d y=0$
Differentiating by parts we will get $(2+y+R)^{2}(1)-y(2)(2+R+y)=0$
Or $2+R+y=2 y$
Or $2+R=y$
For $y=5 \Omega$
$R=3 \Omega$
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