Question

The resistance of a platinum wire at 0°C is 4 Ω. What will be the resistance of the wire at 100°C if the temperature coefficient of resistance of platinum is 0.0038 /°C.

Answer 1

The variation of Resistance with Temperature is given as:

$\boxed{R = R_{\circ} (1+\alpha \Delta T)} \\ \\ \\ OR \quad \boxed{R = R_{\circ}\left(1+\alpha (T-T_{\circ})\right)}$

Here,
$R_{\circ}$ = Resistance at Temperature $T_{\circ}$
$R$ = Resistance at Temperature $T$
$\alpha$ = Coefficient of Resistance



Here, we have the following data from the question:

$T_{\circ} = 0^{\circ} \, \, C \\ \\ T = 100^{\circ} \, \, C \\ \\ R_{\circ} = 4 \, \, \Omega \\ \\ \alpha = 0.0038 \, \, / ^{\circ}C \\ \\ R = \, ?$


We can now find the Resistance of the Platinum Wire at $100^{\circ} \, \, C$



$R = R_{\circ} \left(1 + \alpha (T-T_{\circ})\right) \\ \\ \implies R = 4 (1+0.0038(100-0)) \\ \\ \implies R = 4(1+0.38) \\ \\ \implies R = 4 \times 1.38 \\ \\ \implies \boxed{R = 5.52 \, \, \Omega}$


Thus, the Resistance of Platinum Wire at $\bold{100^{\circ} \, \, C}$ is $\bold{5.52 \, \, \Omega}$