Question

A copper wire of length \( L \) and diameter \( D \) is to be reshaped into another wire so as to have minimum resistance. For this we should

• A. increase \( L \) and decrease \( D \)
• B. decrease \( L \) and increase \( D \)
• C. decrease both \( L \) and \( D \)
• D. increase both \( L \) and \( D \)

Hint:

To minimize the resistance of a wire, its length should be minimized, and the cross-sectional area (related to diameter) should be maximized.

Answer 1

The Correct Option is B

Step 1: Formula for resistance.
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. The area \( A \) is related to the diameter \( D \) by: \[ A = \pi \left( \frac{D}{2} \right)^2 \] Step 2: Minimizing resistance.
For minimum resistance, we need to decrease the length \( L \) and increase the diameter \( D \). This will maximize the area \( A \) and minimize the resistance.
Step 3: Conclusion.
Thus, the correct answer is (B) decrease \( L \) and increase \( D \).