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BITSAT 2015
Exam
BITSAT
Year
2015
Subject
Physics
Chapter
Current Electricity

BITSAT 2015 · Physics · Current Electricity

A constant voltage is applied between the two ends of a uniform...

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

Options

  1. Aboth the length and the radius of the wire are halved.
  2. Bboth the length and the radius of the wire are doubled.
  3. Cthe radius of the wire is doubled.
  4. Dthe length of the wire is doubled.

Correct answer

B. both the length and the radius of the wire are doubled.

Step-by-step solution

The heat produced is given by H=V2R and \frac{V^{2}}{R} \text{ and } R=ρℓπr2∴H=V2(πr2ρℓ)orH=(πV2ρ)r2ℓThusheat\frac{\rho \ell}{\pi r^{2}}\therefore H=V^{2} \left(\frac{\pi r^{2}}{\rho \ell}\right) or \quad H=\left(\frac{\pi V^{2}}{\rho}\right) \frac{r^{2}}{\ell} Thus heat(H)isdoubledifbothlengthis doubled if both length(\ell)andradiusand radius(r)aredoubled.are doubled.
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