Question

Resistance of a wire at temperature t°C is: $R = R_0(1+at+bt^2)$, here, $R_0$ is the resistance at 0°C. Find the temperature coefficient of resistance at temperature 0°C.

• A. a
• B. b
• C. ab
• D. a/b

Answer 1

Answer: (A)

a

Answer 2

The temperature coefficient of resistance $\alpha_t$ is defined as $\frac{1}{R}\frac{dR}{dt}$. Given $R = R_0(1+at+bt^2)$, differentiating with respect to $t$ gives $\frac{dR}{dt} = R_0(a+2bt)$. Substituting $R$ and $\frac{dR}{dt}$ into the formula for $\alpha_t$ and then setting $t=0$ yields $\alpha_0 = \frac{R_0(a+2b(0))}{R_0(1+a(0)+b(0)^2)} = \frac{a}{1} = a$.