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BITSAT 2016
Exam
BITSAT
Year
2016
Subject
Physics
Chapter
Current Electricity

BITSAT 2016 · Physics · Current Electricity

Two resistances at 0^ ^ C with temperature coefficient of...

Two resistances at 0∘C0^{{}^{\circ}} \mathrm{C} with temperature coefficient of resistance α1\alpha_{1} and α2\alpha_{2} joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be

Options

  1. Aα1+α2\alpha_{1}+\alpha_{2}
  2. Bα1α2α1+α2\frac{\alpha_{1} \alpha_{2}}{\alpha_{1}+\alpha_{2}}
  3. Cα1−α22\frac{\alpha_{1}-\alpha_{2}}{2}
  4. Dα1+α22\frac{\alpha_{1}+\alpha_{2}}{2}

Correct answer

D. α1+α22\frac{\alpha_{1}+\alpha_{2}}{2}

Step-by-step solution

R1=R0(1+α1t)+R0(1+α2t)=2R0(1+α1+α22t)\begin{aligned} R_{1} &=R_{0}\left(1+\alpha_{1} t\right)+R_{0}\left(1+\alpha_{2} t\right) \\ &=2 R_{0}\left(1+\frac{\alpha_{1}+\alpha_{2}}{2} t\right) \end{aligned} Comparing with R=R0(1+αt)α=α1+α22R=R_{0}(1+\alpha t)\alpha=\frac{\alpha_{1}+\alpha_{2}}{2}
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