Question

The figure shows a meter bridge with null deflection in the galvanometer. The value of unknown resistance R is?

• A. $158\Omega$
• B. $151.67\Omega$
• C. $128.65\Omega$
• D. $130\Omega$

Answer 1

The correct option is B $151.67\Omega$

From balancing condition of Wheatstone bridge
$\frac{P}{Q}=\frac{R}{S}\Rightarrow \frac{P}{R}=\frac{Q}{S}$ .......(i)
Here, $P=65\Omega$
$R=R=?$
$l_1=30$cm
$l_2=100-30=70$cm
Also, $R=\frac{\rho l}{A}$
In meter bridge, the wire is of uniform cross-section.
So, $R\propto l$
$\therefore \frac{Q}{S}=\frac{l_1}{l_2}$
$\therefore$ From Eq. (i)
$\frac{65}{R}=\frac{l_1}{l_2}=\frac{30}{70}=\frac{3}{7}$
$\therefore R=\frac{65\times 7}{3}=\frac{455}{3}=151.67\Omega$.