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:

For constant voltage, heat produced is inversely proportional to resistance.

Answer 1

The Correct Option is A

Step 1: Heat produced: H = (V² t)/(R)
Step 2: Resistance of wire: R = ρ(L)/(A) = ρ(L)/(π r²)
Step 3: If L → L/2 and r → r/2: R' = ρ(L/2)/(π(r/2)²) = 2R H' = (V² t)/(R/2) = 2H