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

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

1 + x = $p^{2}$

p = $\sqrt{1 +x}$

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