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 = $$ \sqrt{1 +x}$$