Question

The graph between variation of resistance of a wire as a function of its diameter keeping other parameters like length and temperature constant is 

• A.
• B.
• C.
• D.

Hint:

Resistance of a wire is inversely proportional to the cross-sectional area. Since area depends on the square of the diameter, resistance decreases as the diameter increases.

Answer 1

The Correct Option is C

The resistance \( R \) of a wire is given by the formula: \[ R = \rho \frac{L}{A} \] where \( \rho \) is the resistivity, \( L \) is the length, and \( A \) is the cross-sectional area of the wire. For a wire with a circular cross-section, the area \( A \) is given by: \[ A = \pi \left(\frac{D}{2}\right)^2 = \frac{\pi D^2}{4} \] Thus, the resistance is inversely proportional to the square of the diameter \( D \), meaning as the diameter increases, the resistance decreases. Therefore, the graph of resistance vs. diameter will show a decreasing trend as diameter increases. The correct graph will show a decrease in resistance as \( D \) increases.