A Creative Discussion on Electrical Resistance

What happens when a coffee cup heater and a lamp are connected in parallel to the same 120-V outlet?

How do we calculate the resistance of the lamp in this scenario?

Understanding Electrical Resistance in Parallel Circuits

When a coffee cup heater and a lamp are connected in parallel to the same 120-V outlet, they share the total power consumption of 110 W. The resistance of the coffee cup heater is given as 540Ω. To find the resistance of the lamp, we need to utilize the formula for calculating total resistance in a parallel circuit.

Let's assume the resistance of the lamp is RL. The total resistance in the circuit can be calculated as:

1/RTotal = 1/Rheater + 1/RL

By substituting the given values, we can rearrange the equation to find the resistance of the lamp.

Calculating the Resistance of the Lamp

Given that the total power consumed is 110 W and both the coffee cup heater and lamp share the same voltage of 120 V, we can derive the resistance of the lamp by rearranging the formula.

First, we calculate the total resistance in the circuit using the power formula:

P = V^2 / RTotal = 110 = 120^2 / RTotal

Solving for RTotal, we get RTotal = (120^2) / 110.

Substituting this value back into the equation for RL, we simplify the calculation:

1/RL = 1/RTotal - 1/Rheater = 1/((120^2) / 110) - 1/540

After simplifying the equation, we can find the reciprocal of both sides to determine the resistance of the lamp:

RL = 1 / (110 / (120^2) - 1/540)

Calculating the value of RL, we find it to be approximately 0.0006 Ω.

For further explanations on calculating resistance in a parallel circuit, you can explore additional resources.