Answer to Question #243182 in Electrical Engineering for Jac

Question

A resistive coil draws 2A at 110 V after operating for a long time. If the temperature rise is 55°C above the ambient temperature of 20°C, calculate the external resistance which must be initially connected in series with the coil to limit the current to 2A. The temperature coefficient of the material of the coil is 0.0043 per °C at 20°C.

Answer 1

For the "hot" condition, we have

$$I=\frac{V}{R_0(1+\alpha T)},\\\space\\ R_0=\frac{V}{I(1+\alpha T)}.$$

For the cold condition, we have

$$I=\frac{V}{R_0+r}.$$

Equate:

$$\frac{V}{R_0(1+\alpha T)}=\frac{V}{R_0+r},\\\space\\ r=R_0(1+\alpha T)-R_0,\\\space\\ r=R_0\alpha T=\frac{V\alpha T}{I(1+\alpha T)}=7.19\Omega.$$