Answer to Question #165129 in Electric Circuits for Sarah

Question

A nickel wire has a resistance of 26.4 ohms at 60 degrees Celsius. After several hours of cooling, the resistance of the coil has decreased to 20 ohms. What is the new temperature of the wire?

Answer 1

$R_o=26.4\Omega\\ T_o=60^{\circ} C\\ R_t=20\Omega$

$\alpha = -0.006$ (as the temperature is decreasing)

Let T be the new temperature of the wire

We know,

$R_t=R_o(1+\alpha\Delta T)$

Putting the values of $R_o,T_o and R_t$

$20=26.4(1-0.006(60-T_o))$

$40.40=60-T$

$T=39.6^\circ C$

Hence,the new temperature of wire is $39.6^\circ C$