In her bathroom, Mindy has an overhead heater that consists of a coiled wire made of nichrome that gets hot when turned on. The wire has a length of 3.0 m when it is uncoiled. The heating element is attached to the normal 120-V wiring and when the wire is glowing red hot it has a temperature of about 420 ° C and dissipates 2200 W of power. Nichrome has a resistivity of 108 × 10−8 Ω · m at 20 ° C and a temperature coefficient of resistivity of 0.00040 ° C−1.
(a) What is the resistance of the heater when it is turned on?
(b) What current does the wire carry?
(c) If the wire has a circular cross section, what is its diameter? Ignore the small changes in the wire's diameter and length due to changes in temperature.
(d) When the heater is first turned on, it has not yet heated up, so it is operating at 20 ° C. What is the current through the wire when it is first turned on?