Question

A potentiometer wire has length 4 m and resistance \(8\ \Omega\). The resistance that must be connected in series with the wire and the driving battery of e.m.f. 2 V, so as to get a potential gradient of 1 mV per cm on the wire is

• A. \(50\ \Omega\)
• B. \(42\ \Omega\)
• C. \(40\ \Omega\)
• D. \(32\ \Omega\)

Hint:

Find the voltage across the wire from the gradient, then the current, then the extra resistance from the battery emf.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Gradient \(=1\ \text{mV/cm}=0.1\ \text{V/m}\). Over 4 m, the voltage across the wire is \(0.4\ \text{V}\).

Step 2: Current
\(I=\dfrac{0.4}{8}=0.05\ \text{A}\)

Step 3: Series resistance
Total resistance \(=\dfrac{2}{0.05}=40\ \Omega\).
\(R=40-8=32\ \Omega\)

Final Answer:
A resistance of 32 ohm must be connected in series. \[ \boxed{\text{(D) }32\ \Omega} \]