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Four Resistances $P, Q, R, X$ formed a wheat stone bridge. The bridge is balanced when $R = 100 Ω$ .If P and Q are inter changed the bridge balance for $121 Ω$ .The value of X is

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Correct option is D

Resistance $R = 100 Ω$ Resistance $R = 121 Ω$
Balancing condition for wheat stone bridge
$\frac{P}{Q} = \frac{R}{X} \Rightarrow \frac{P}{Q} = \frac{100}{X} . . . (1)$

$P and Q are inter changed \frac{Q}{P} = \frac{R}{X} \frac{Q}{P} = \frac{121}{X} . . . . (2)$

$on 1 \times 2 we get \frac{P}{Q} \times \frac{Q}{P} = \frac{100}{X} \times \frac{121}{X} \Rightarrow 1 = \frac{100}{X} x \frac{121}{X} ∴ X = 110 Ω$

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Four Resistances P,Q,R,X formed a wheat stone bridge. The bridge is balanced when R=100 Ω .If P and Q are inter changed the bridge balance for121 Ω .The value of X is