Q: Resistance of a wire at temperature t °C is R = R_{0}(1 + a t + b t^{2})

Here, R_{0} 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)} $