Question

A wire has a length of 2 m and resistance of \(10\,\Omega\). It is connected in series with a resistance of \(990\,\Omega\) and a cell of e.m.f. 2 V. The potential gradient along the wire will be

• A. \(0.01\,\text{V/m}\)
• B. \(0.1\,\text{V/m}\)
• C. \(1\,\text{V/m}\)
• D. \(10\,\text{V/m}\)

Hint:

Potential gradient = potential drop per unit length.

Answer 1

The Correct Option is A

Step 1: Total resistance of the circuit.
\[ R_{\text{total}} = 10 + 990 = 1000\,\Omega \]
Step 2: Current in the circuit.
\[ I = \frac{V}{R_{\text{total}}} = \frac{2}{1000} = 0.002\,\text{A} \]
Step 3: Potential drop across the wire.
\[ V_{\text{wire}} = I \times R_{\text{wire}} = 0.002 \times 10 = 0.02\,\text{V} \]
Step 4: Potential gradient.
\[ \text{Potential gradient} = \frac{0.02}{2} = 0.01\,\text{V/m} \]
Step 5: Conclusion.
The potential gradient along the wire is 0.01 V/m.