A Wheatstone's bridge is balanced with a resistance of 625, Omega in the third arm, where P, Q and S are in the 1^{st}, 2^{nd}

Q: $A$ Wheatstone's bridge is balanced with a resistance of $625\, \Omega$ in the third arm, where $P, Q$ and $S$ are in the $1^{st}, 2^{nd}$ and $4^{th}$ arm respectively. If $P$ and $Q$ are interchanged, the resistance in the third arm has to be increased by $51\,\Omega$ to secure balance. The unknown resistance in the fourth arm is ............. $\Omega$

b The balancing condition for Wheatstone's bridge is, $\frac{P}{Q}=\frac{S}{R}$ $\frac{P}{Q}=\frac{625}{R}$$.....................(1)$ When $\mathrm{P}$ and $\mathrm{Q}$ are interchanged we get, $\frac{Q}{P}=\frac{676}{R}$ $\frac{P}{Q}=\frac{R}{676}$$.....................(2)$ Equating both the equations, $\frac{P}{Q}=\frac{625}{R}=\frac{R}{676}$ $R^{2}=\sqrt{422500}$ $R=650 \Omega$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

$A$ Wheatstone's bridge is balanced with a resistance of $625\, \Omega$ in the third arm, where $P, Q$ and $S$ are in the $1^{st}, 2^{nd}$ and $4^{th}$ arm respectively. If $P$ and $Q$ are interchanged, the resistance in the third arm has to be increased by $51\,\Omega$ to secure balance. The unknown resistance in the fourth arm is ............. $\Omega$

A$625$
B$650$
C$676$
D$600$

Diffcult

STD 11 Science
JEE
STD 12 - 3. current electricity
Physics

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