The electric fireplace is made of nickel wire 50 m long and 1.4 mm squared, determine the power consumed

The electric fireplace is made of nickel wire 50 m long and 1.4 mm squared, determine the power consumed by the fireplace if the mains voltage is 120 V.

Given:

L = 50 meters – the length of the nickel wire;

S = 1.4 square millimeters – wire cross-section;

U = 120 Volts – mains voltage;

k = 0.4 Ohm * mm2 / m is the specific resistance of nickelin.

It is required to determine W (Watt) – the power of the electric fireplace.

Determine the resistance of the nickel wire:

R = k * L / S = 0.4 * 50 / 1.4 = 20 / 1.4 = 14.3 Ohm.

Then the current in the circuit will be equal to:

I = U / R = 120 / 14.3 = 8.4 Amperes.

The power of an electric fireplace will be equal to:

W = U * I = 120 * 8.4 = 1008 W = 1 kW.

Answer: the power of an electric fireplace is 1 kW.