Question

A 500-W heating coil designed to operate from 110V is made of Nichrome wire 0.500 mm in diameter. (a) Assuming the resistivity of the Nichrome remains constant at its 20.0°C value, find the length of wire used.

Answer 1

The length of the wire used is 3.162 m

Resistivity of a material

The formula for calculating the power is expressed as;

P = V²/R

Determine th resistance

R =  V²/P

Determine the resistance of the heating coil by substituting

R = (110²/500)

R = 12100/500

R = 24.2ohms

Determine the length of the wire

R = ρL/A such that;

L = RA/ρ

Substitute the given parameters

diameter = 0.5 mm = 0.0005m

radius = 0.0005/2 = 0.00025 m

Determine the area

A = πr²

A = π * 0.00025²

A = 1.96*10^-7 m²

Determine the length

L = (24.2 * 1.96*10^-7 / 1.50*10^-6) =

L = 3.162 m

Hence the length of the wire used is 3.162 m

The length of the wire used is 3.162 m

Learn more on resistivity here; brainly.com/question/24858512

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