Question

In case of meter bridge experiment balance length for $2\Omega$ and $3\Omega$ is $\ell$ and for $x\Omega$ and $3\Omega$ is $(\ell + 10)$ cm. Find $x$.

Hint:

Always substitute the balance length correctly while applying the meter bridge ratio formula.

Answer 1

Correct Answer: 30

Step 1: Meter bridge balance condition.
In a meter bridge, the balance condition is given by:
\[ \dfrac{R_1}{R_2} = \dfrac{\ell}{100 - \ell} \]
Step 2: Applying given data for $2\Omega$ and $3\Omega$.
\[ \dfrac{2}{3} = \dfrac{\ell}{100 - \ell} \]
Solving,
\[ 3\ell = 200 - 2\ell \Rightarrow \ell = 40 \text{ cm} \]
Step 3: Applying condition for $x\Omega$ and $3\Omega$.
New balance length = $\ell + 10 = 50$ cm
\[ \dfrac{x}{3} = \dfrac{50}{100 - 50} = \dfrac{50}{50} = 1 \]
Step 4: Calculating value of $x$.
\[ x = 3 \times 1 = 30\Omega \]