Question

Figure 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 $400\text{mm}$ and $588\text{mm}$ when $X$ is connected to $Y$ and $Z$, respectively. The length of the slide wire is $1.0\text{m}$. 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 $47\Omega$

Given:
$l_1=400\text{mm};l_2=588\text{mm}$

Let $K$ be the potential gradient of in the wire.

When $X$ is connected to $Y$, the balance length $l_1$ is proportional to the p.d. across the $100\Omega$ resistor.

$K\left(400\right)\propto 100........\left(1\right)$

Similarly, when $X$ is connected to $Z$, the balance length is proportional to the p.d. across the $100\Omega$ resistor and resistor $R$.

$K\left(588\right)\propto (100+R)........\left(2\right)$

Dividing eq. $\left(1\right)$ to $\left(2\right)$, we get

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

$R=47\Omega$

Hence, option $\left(b\right)$ is correct.

Key concept:- If a constant current flows through a wire of uniform area of cross-section, then the potential drop along the wire is directly proportional to the length of the wire.