Connect a Coffee Cup Heater and a Lamp in Parallel
What is the total power used when a coffee cup heater and a lamp are connected in parallel? What is the resistance of the lamp?
The coffee cup heater and lamp are connected in parallel to a 120 V outlet, using a total of 98 W of power. The resistance of the coffee cup heater is 770 Ω.
Total Power and Resistance Calculation
When devices are connected in parallel, the voltage across each device is the same, while the currents add up. The resistance of the lamp is approximately 146.78 Ω.
When devices are connected in parallel, the voltage across each device is the same, while the currents add up. We know that the total power consumed by both devices is 98 W and the resistance of the coffee cup heater is 770 Ω. To find the resistance of the lamp, we can use the formula P = IV, where P is power, I is current, and V is voltage.
Let's solve for the current flowing through the coffee cup heater:
Using the formula P = IV, we can rewrite this as V = P/I. Plugging in the values, we get 120 = 98/I.
Simplifying the equation, we find I = 98/120 = 0.817 A. Since the devices are connected in parallel, the current flowing through the lamp will also be 0.817 A.
Now, let's find the resistance of the lamp by using Ohm's Law, which states that resistance (R) is equal to voltage (V) divided by current (I):
Let's plug in the values: R = 120/0.817 = 146.78 Ω.