Afish-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?

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 = 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.

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explanation: