Question

Figure below shows a circuit which may be used to compare the resistance $R$ of an unknown resistor with a $100\Omega$ standard. The distances $l$ from one end of the potentiometer slider wire to the balance point are 400 mm and 588 mm when X is connected to Y and Z respectively. The length of the slide is 1.00 m. What is the value of resistance R?

• A. $32\Omega$
• B. $47\Omega$
• C. $68\Omega$
• D. $147\Omega$

Answer 1

The correct option is B $47\Omega$

In first case when the circuit is connected to point Y
Let $\varphi$ be the resistance per unit length and $i$ be the current flowing through the potentiometer.
So, we can write
$i\times 100\Omega =\varphi \times 400\times {10}^{-3}\times i$.....(i)
Case:2
When the potentiometer is connected to point Z
$⟹i_1\times (100+R)=\varphi \times 588\times {10}^{-3}\times i_1$..(ii)
On dividing (i) and (ii) we get

$\frac{100}{100+R}=\frac{400}{588}$

On further solving this we get
$R=47$ $\Omega$