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

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

Option: 1

R=R_0(6 T+2)


Option: 2

R=2 R_0(3+2 T)


Option: 3

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


Option: 4

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


Answers (1)

best_answer

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

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Rishi

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