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 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:
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At constant voltage:
\[
H\propto \frac{1}{R}
\]
Changing radius affects resistance quadratically.
Updated On: Mar 23, 2026
- both the length and the radius of the wire are halved
- both the length and the radius of the wire are doubled
- the radius of the wire is doubled
- the length of the wire is doubled
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The Correct Option is C
Solution and Explanation
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).
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