Resistance of a wire at temperature `t^(@)C` is
`R = R_(0)(1+at+bt^(2))`
Here, `R_(0)` is the temperature at `0^(@)C`. The temperature coefficient of resistance at temperature t is

Options

A. `((1+alphat+betat^2))/(alpha+2beta t)`
B. `(alpha+2beta t)`
C. `(alpha +2 beta t)/((1 +alphat + beta t^2))`
D. `(alpha +2betat)/(2(1+alpaht +beta r^2))`

Answer

C

Explanation

`alpha = (1)/(R_(t))(dR_(t))/(dt) = (1)/(R_t)=(1)/(R_t) R_0 [ alpha +2betat]`
`alpha=(R_(0)[alpha+2betat])/(R_(0)[1+alpha t+betat^(2)])=(alpha+2betat)/(1+alpha t+beta t^(2))`