The resistance of a conductor at 15^{circ}C i | vedclass

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(D) The resistance of a conductor at temperature $T$ is given by the formula: $R_T = R_0(1 + \alpha \Delta T)$,where $R_0$ is the resistance at $0^{\c

Vedclass · Accepted Answer

$0.003\, ^{\circ}C^{-1}$

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(D) The resistance of a conductor at temperature $T$ is given by the formula: $R_T = R_0(1 + \alpha \Delta T)$,where $R_0$ is the resistance at $0^{\circ}C$,$\alpha$ is the temperature coefficient of resistance,and $\Delta T$ is the change in temperature.Given:$R_1 = 16\, \Omega$ at $T_1 = 15^{\circ}C$$R_2 = 20\, \Omega$ at $T_2 = 100^{\circ}C$Using the relation $R_T = R_0(1 + \alpha T)$:$16 = R_0(1 + 15\alpha)$  --- (Equation $1$)$20 = R_0(1 + 100\alpha)$ --- (Equation $2$)Dividing Equation $2$ by Equation $1$:$\frac{20}{16} = \frac{1 + 100\alpha}{1 + 15\alpha}$$1.25(1 + 15\alpha) = 1 + 100\alpha$$1.25 + 18.75\alpha = 1 + 100\alpha$$0.25 = 81.25\alpha$$\alpha = \frac{0.25}{81.25} \approx 0.00307\, ^{\circ}C^{-1}$Rounding to the nearest value,we get $\alpha \approx 0.003\, ^{\circ}C^{-1}$.

The resistance of a conductor at $15^{\circ}C$ is $16\, \Omega$ and at $100^{\circ}C$ is $20\, \Omega$. What will be the temperature coefficient of resistance of the conductor?

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