Question

A resistance of $2\Omega$ is connected across one gap of a meter-bridge (the length of the wire is $100cm$) and an unknown resistance, greater than $2\Omega$, is connected across the other gap. When these resistances are interchanged, the balance point shifts by $20cm$. Neglecting any corrections, the unknown resistance is

• A. $3\Omega$
• B. $4\Omega$
• C. $5\Omega$
• D. $6\Omega$

Answer 1

Answer: (A)

$R>2\Omega \Rightarrow \therefore 100-x>x$
$Applying\frac{P}{Q}=\frac{R}{S}$
$Wehave\frac{2}{R}=\frac{x}{100-x}...(i)$
$\frac{R}{2}=\frac{x+20}{80-x}...(ii)$
$SolvingEqs.(i)and(ii),weget,R=3\Omega$
$\therefore$Correct option is (a).