Resistance of a wire at temperature t^° C is R = R_0(1 + a t + bt^2) Here, R_0 is the temperature at 0^°C…

Q: Resistance of a wire at temperature t °C is R = R0(1 + a t + b t2)
Here, R0 is the temperature at 0 °C. Find the temperature coefficient of resistance at temperature t is

Sol: $\large \alpha = \frac{1}{R} \frac{dR}{dt} $

$\large \alpha = \frac{1}{R_0(1+at+bt^2)} \frac{d(R_0(1+at+bt^2))}{dt} $

$\large \alpha = \frac{1}{R_0(1 + at + bt^2)} (R_0(a + 2bt)) $

$\large \alpha = \frac{(a + 2bt)}{(1+at+bt^2)} $