GATE 2015 EE - SET 1 Question - 30

Solution :

V_{0}=\left [ \frac{R(1+x)}{PR+R(1+x)} - \frac{R}{R+PR}\right ] E

V_{0} =\left [ \frac{(1+x)}{P+(1+x)} - \frac{1}{1+P}\right ] E

V_{0} = \left [ \frac{1+P+x+xp_1-x-p}{1+P+x+P+px+p^{2}} \right ] E

V_{0} = \left [\frac{xp} {1+x+2P+px+p^{2}} \right ]E

V_{0} = \left [\frac{xp}{1+x+P+(2+x+p)} \right ]E

\frac{dV_{o}}{dP} = \frac{xp\left [ 2+x+p \right ]-\left [ 1+x+p^{2}+xp+2p \right ](x)}{(1+x+p^{2}+xp+2p)^{2}}

xp (2+x+2p) = (1+x+P^{2}+xp +2p)x

2p+xp+2p^{2} = 1 + x + p^{2}+ xp + 2p

2p^{2} = 1 + x + p^{2}

1 + x =  p^{2}

p =  \sqrt{1 +x}