Question

A meter bridge setup as shown below is used to determine an unknown resistance $\text{X}$ using a standard $21\Omega$ resistor. If null point is at $40\text{cm}$ from $\text{A}$, and end correction at $\text{A, B}$ are $2.0\text{cm}$ each, find value of $\text{X}$,

• A. $21\Omega$
• B. $31\Omega$
• C. $41\Omega$
• D. $51\Omega$

Answer 1

The correct option is B $31\Omega$

Using the concept of proportion between the lengths and their respective resistances we can write,

$\frac{R}{l_1}=\frac{X}{l_2}$

Since, $l_1=40+2=42\text{cm}$, and $l_2=60+2=62\text{cm}$

$\frac{R}{40+2}=\frac{X}{60+2}$

$X=\frac{21}{42}\times 62$

$X=31\Omega$