A Lamp and a Coffee Maker Connected in Parallel

19 May 2023

What is the resistance of the lamp connected in parallel to a coffee maker with a resistance of 300 Ohm and both using a total of 140 W of power?

Resistance of the lamp (r) = 156.52 ohm (Approx.)

Calculation of Resistance of the Lamp

Given:
Total power p = 140 W
Resistance of the coffee maker = 300 Ohm
Voltage v = 120 V

Find:
Resistance of the lamp (r)

Computation:

We know that
p = v² / R

So,
Total power p = [Voltage² / Resistance of the lamp (r)] + [Voltage² / Resistance of the coffee maker]

140 = [120² / r] + [120² / 300]

140 = 120² [1/r + 1/300]

Resistance of the lamp (r) = 156.52 ohm (Approx.)