Question

A heater is being designed that uses a coil of 14-gauge nichrome wire to generate 300 W using a voltage of V = 110 V . How long should the engineer make the wire?(Note 14-guage wire has a diameter of 1.63 mm.)

Answer 1

The length of the wire is 83.2 m.

Step-by-step explanation:

Given that,

Power of heater, P = 300 W

Voltage, V = 110 V

The resistivity of nichrome wire is,
`\rho=100* 10^(-8)\ \Omega-m`

The electric power of a wire is given by :

`P=(V^2)/(R)\\\\R=(V^2)/(P)\\\\R=((110)^2)/(300)\\\\R=40.34\ \Omega`

Area of cross section of the wire is :

`A=\pi r^2\\\\A=\pi (0.000815)^2\\\\A=2.08* 10^(-6)\ m^2`

Resistance of a material is given by :

`R=\rho (L)/(A)\\\\L=(RA)/(\rho)\\\\L=(40* 2.08* 10^(-6))/(10^(-6))\\\\L=83.2\ m`

So, the length of the wire is 83.2 m. Hence, this is the required solution.