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  • The temperature coefficient of resistance of conductor varies as <img alt="\mathrm{\alpha(T)=3 T^2+2 T}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Calpha%28T%29%3D3%20T%5E2

The temperature coefficient of resistance of conductor varies as \mathrm{\alpha(T)=3 T^2+2 T}. If \mathrm{R_0} is resistance at \mathrm{T=0} and R is resistance at T, then
 

Option: 1

\mathrm{R=R_0(6 T+2)}


Option: 2

\mathrm{R=2 R_0(3+2 T)}


Option: 3

\mathrm{R=R_0\left(1+T^2+T^3\right)}


Option: 4

\mathrm{R=R_0\left(1-T+T^2+T^3\right)}


Answers (1)

best_answer

\begin{aligned} &\mathrm{ a(T)=\frac{1}{R_0} \frac{d R}{d T} \Rightarrow\left(3 T^2+2 T\right)=\frac{1 d R}{R_0 d T} }\\ &\mathrm{ \Rightarrow d R=R_0\left(3 T^2+2 T\right) d T }\\ &\mathrm{ \Rightarrow \int_{R_0}^R d R \mid=R_0\left[3 \int_0^T T^2 d T+2 \int_0^T T d T\right] }\\ &\mathrm{ \Rightarrow R=R_0\left[1+T^2+T^3\right]}\\ \end{aligned}

Posted by

Irshad Anwar

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