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AIIMS 2015
Exam
AIIMS
Year
2015
Subject
Physics
Chapter
Current Electricity

AIIMS 2015 · Physics · Current Electricity

When a current is passed in a conductor, 5^ C rise in temperature...

When a current is passed in a conductor, 5∘C5^{\circ} \mathrm{C} rise in temperature is observed. If the strength of current is made thrice, rise in temperature will be

Options

  1. A5∘C5^{\circ} \mathrm{C}
  2. B20∘C20^{\circ} \mathrm{C}
  3. C45∘C45^{\circ} \mathrm{C}
  4. D15∘C15^{\circ} \mathrm{C}

Correct answer

C. 45∘C45^{\circ} \mathrm{C}

Step-by-step solution

Joule heating in a wire, H=I2RtH=I^2 R t For given Randt,H∝I2R and t, H \propto I^2 \therefore H1H2=I12I22Also,\frac{H_1}{H_2}=\frac{I_1^2}{I_2^2}Also,H=m s \Delta TForgivenFor givenm and s, H \propto \Delta T∴H1H2=ΔT1ΔT2Fo\therefore \frac{H_1}{H_2}=\frac{\Delta T_1}{\Delta T_2}For eqn. (i)and(ii)I12I22=ΔT1ΔT2Here,and (ii)\frac{I_1^2}{I_2^2}=\frac{\Delta T_1}{\Delta T_2}Here,I_1=I, \Delta T_1=5^{{}^{\circ}} C\mathrm{C}, I_2=3 IΔT2=?∴(I3I)2=5ΔT2 or  \DeltaT2=45∘C\begin{aligned}& \Delta T_2=? \\ & \therefore \left(\frac{I}{3 I}\right)^2=\frac{5}{\Delta T_2} \text{\text{ or } } \DeltaT_2=45^{{}^{\circ}} \mathrm{C} \end{aligned}
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