Question

A fish-tank heater is rated at 96 W when connected to 120 V. The heating element is a coil of Nichrome wire. When uncoiled, the wire has a total length of 4.2 m . What is the diameter of the wire?

Answer 1

Answer:

0.232 mm.

Explanation:

Power, P = 96 W

Voltage, V = 120 V

Length of wire, l = 4.2 m

Let r be the radius of the wire.

Resistivity of nichrome, ρ = 1.5 x 10^-6 ohm metre

P = V^2 / R

R = 120 x 120 / 96 = 150 ohm

$R = \rho \frac{l}{A}=\rho \frac{l}{\pi r^{2}}$

$r^2= \rho \frac{l}{\pi \times R}$

$r^2= \1.5\times10^{-6} \frac{4.2}{3.14 \times 150}$

r = 1.16 x 10^-4 m

Diameter = 2 x r = 2 x 1.16 x 10^-4 = 2.32 x 10^-4 m = 0.232 mm

Thus, the diameter of the wire is 0.232 mm.