Question

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 on the third arm has to be increased by $51\Omega$ to secure balance. The unknown resistance in the fourth arm is

• A. $625\Omega$
• B. $650\Omega$
• C. $676\Omega$
• D. $600\Omega$

Answer 1

The correct option is B $650\Omega$

The balancing condition for Wheatstone's bridge is,
$\frac{P}{Q}=\frac{S}{R}$
$\frac{P}{Q}=\frac{625}{R}$ ....................................(1)
When P and Q are interchanged we get,
$\frac{Q}{P}=\frac{676}{R}$
$\frac{P}{Q}=\frac{R}{676}$ ..............................(2)

Equating both the equations,

$\frac{P}{Q}=\frac{625}{R}=\frac{R}{676}$

$R^2=\sqrt{422500}$

$R=650\Omega$