In her bathroom, Mindy has an overhead heater that consists of a coiled wire mad
ID: 2053806 • Letter: I
Question
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 3.5 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 411° C and dissipates 2275 W of power. Nichrome has a resistivity of 1.08 10-6 m at 20° C and a temperature coefficient of resistivity of 0.00040° C -1.(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.
Explanation / Answer
P=V^2/R R=6.32 resistivity=1.08*10^-6(1+0.0004*(411-20)) =1.08*1.15*10^-6 =1.2*10^-6 R=res*l/a a=res*l/R =6.64 *10^-7 d^2=6.64*4*10^-7/3.14 d=9.19*10^-4 0.919 mm