Question

Figure shows a potentiometer in which R is variable resistance. AB is uniform wire of length 100 cm having resistance ‘r’. In an experiment R = 0, then null deflection is at 30 cm from A and for R = x, null deflection is at 60 cm from A. The value of x is

• A. $\frac{r}{2}$
• B. $\frac{3r}{2}$
  
• C. $2r$
  
• D. $r$

Answer 1

The correct option is D $r$

When R = 0

$10\propto 100$

and $E\propto 30$

$\Rightarrow \frac{10}{E}=\frac{100}{30}$ (or) $E=3$ volt

When R = x :

P.D across the wire is 10 - V where V is P.D across R.
$10-V\propto 100$ and $3\propto 60$

$\Rightarrow \frac{10-V}{3}=\frac{100}{60}\Rightarrow V=5$ volt.

Let i1 be the current through primary circuit, then
$i_1=\frac{10}{r+x}$
and P.D across resistor is $V=i_{1}x$

$5=\left(\frac{10}{r+x}\right)x$

$5r+5x=10x$

$\Rightarrow x=r$