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:

The length of the wire is 83.2 m.

Explanation:

Given that,

Power of heater, P = 300 W

Voltage, V = 110 V

The resistivity of nichrome wire is, [tex]\rho=100\times 10^{-8}\ \Omega-m[/tex]

Answer:The length of the wire is 83.2 m.

Explanation:Given that,

Power of heater, P = 300 W

Voltage, V = 110 V

The resistivity of nichrome wire is, [tex]\rho=100\times 10^{-8}\ \Omega-m[/tex]

The electric power of a wire is given by :

[tex]P=\dfrac{V^2}{R}\\\\R=\dfrac{V^2}{P}\\\\R=\dfrac{(110)^2}{300}\\\\R=40.34\ \Omega[/tex]

Area of cross section of the wire is :

[tex]A=\pi r^2\\\\A=\pi (0.000815)^2\\\\A=2.08\times 10^{-6}\ m^2[/tex]

Resistance of a material is given by :

[tex]R=\rho \dfrac{L}{A}\\\\L=\dfrac{RA}{\rho}\\\\L=\dfrac{40\times 2.08\times 10^{-6}}{10^{-6}}\\\\L=83.2\ m[/tex]

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