Question

A wire of length $100~\mathrm{cm}$ is connected to a cell of emf $2\mathrm{V}$ and negligible internal resistance. The resistance of the wire is $3\Omega$. The additional resistance required to produce a potential difference of $1\mathrm{mV / cm}$ is}

• A. $60\Omega$
• B. $47\Omega$
• C. $57\Omega$
• D. $35\Omega$

Hint:

Potential gradient $k = \frac{V}{L}$, and $I = \frac{E}{R_{total}}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Potential gradient $k = \frac{V}{L}$, and $I = \frac{E}{R_{total}}$.
Step 2: Detailed Explanation:
Required potential gradient $k = 1$ mV/cm $= 0.1$ V/m. Total potential drop across wire $= k \times L = 0.1 \times 1 = 0.1$ V. Current $I = \frac{V}{R_{wire}} = \frac{0.1}{3} = \frac{1}{30}$ A. Total resistance in circuit $= \frac{E}{I} = \frac{2}{1/30} = 60\Omega$. Additional resistance $= 60 - 3 = 57\Omega$.
Step 3: Final Answer:
The additional resistance required is $57\Omega$.