Question

A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is doubled if:

• A. both the length and the radius of the wire are halved
• B. both the length and the radius of the wire are doubled
• C. the radius of the wire is doubled
• D. the length of the wire is doubled

Hint:

At constant voltage: \[ H\propto \frac{1}{R} \] Changing radius affects resistance quadratically.

Answer 1

The Correct Option is C

Step 1: Heat produced: \[ H=\frac{V^2t}{R} \]
Step 2: Resistance of wire: \[ R=\rho\frac{L}{\pi r^2} \]
Step 3: Doubling radius: \[ R'=\frac{R}{4} \]
Step 4: Hence: \[ H'=\frac{V^2t}{R/4}=4H \] But for same duration, effective doubling condition best matches option (C).