Coffee Cup Heater and Lamp Connected in Parallel

What is the total power used by a coffee cup heater and a lamp connected in parallel to a 120-V outlet?

Total power used: 78 W

What is the resistance of the heater in this setup?

Resistance of the heater: 8100 ohms

How can we find the resistance of the lamp in this circuit?

Calculation of the Resistance of the Lamp

The resistance of the lamp is approximately 188.89 ohms.

In this setup, a coffee cup heater and a lamp are connected in parallel to the same 120-V outlet. The total power used by both the heater and the lamp is 78 W. The resistance of the heater is 8100 ohms.

To find the resistance of the lamp, we can use the formula for calculating the total resistance of resistors connected in parallel, which is 1/RTotal = 1/R1 + 1/R2.

Let's assume the resistance of the lamp is RL. Since the resistance of the heater is 8100 ohms, we can calculate the power used by the lamp using the power formula: PLamp = V^2 / RL.

Since both the heater and the lamp are connected in parallel to the same 120-V outlet, the voltage is the same for both, which is 120 V. Using this information, we can find the power used by the heater (1.7778 W) and then calculate the power used by the lamp (76.2222 W).

By substituting the known values into the power formula for the lamp (PLamp = 120^2 / RL), we can simplify the equation and solve for RL. The resistance of the lamp is approximately 188.89 ohms.