A coffee maker is rated at 1200 W, a toaster at 1100 W, and a waffle maker at
1400 W. The three appliances are connected in parallel to a common 120-V household circuit. (a) What is
the current in each appliance when operated independently? (b) What total current is delivered to the
appliances when all are operating simultaneously? (c) Is a 15-A circuit breaker sufficient in this situation?
Explain.
To calculate the current in each appliance, we can use Ohm's Law, which states that current (I) is equal to power (P) divided by voltage (V).
(a) When each appliance is operated independently:
For the coffee maker:
Power (P) = 1200 W
Voltage (V) = 120 V
Using the formula I = P / V, we can calculate the current:
I[coffee maker] = 1200 W / 120 V = 10 A
For the toaster:
Power (P) = 1100 W
Voltage (V) = 120 V
Using the formula I = P / V, we can calculate the current:
I[toaster] = 1100 W / 120 V = 9.17 A
For the waffle maker:
Power (P) = 1400 W
Voltage (V) = 120 V
Using the formula I = P / V, we can calculate the current:
I[waffle maker] = 1400 W / 120 V = 11.67 A
(b) To find the total current delivered to the appliances when all are operating simultaneously, we need to add up the individual currents:
Total current = I[coffee maker] + I[toaster] + I[waffle maker]
Total current = 10 A + 9.17 A + 11.67 A = 30.84 A
(c) A 15-A circuit breaker is not sufficient in this situation. The total current required when all appliances are operating simultaneously is 30.84 A, which exceeds the maximum current that can be provided by a 15-A circuit breaker.
To answer these questions, we need to use Ohm's Law and the concept of power.
(a) To find the current in each appliance when operated independently, we can use the formula:
Current (I) = Power (P) / Voltage (V)
For the coffee maker:
I₁ = 1200 W / 120 V = 10 A
For the toaster:
I₂ = 1100 W / 120 V = 9.17 A
For the waffle maker:
I₃ = 1400 W / 120 V = 11.67 A
Therefore, the current in each appliance when operated independently is 10 Amps for the coffee maker, 9.17 Amps for the toaster, and 11.67 Amps for the waffle maker.
(b) To find the total current delivered to the appliances when all are operating simultaneously, we simply add up the individual currents:
Total Current = I₁ + I₂ + I₃ = 10 A + 9.17 A + 11.67 A = 30.84 A
So, the total current delivered to the appliances when they are all operating together is 30.84 Amps.
(c) To determine if a 15-A circuit breaker is sufficient, we compare the total current (30.84 A) to the rating of the circuit breaker (15 A). Since the total current exceeds the circuit breaker rating, a 15-A circuit breaker is not sufficient in this situation.
In order to handle the total current required for all three appliances, you would need a circuit breaker with a rating greater than or equal to 30.84 Amps, such as a 40-A circuit breaker.
Remember, when calculating the total current, appliances connected in parallel add up their individual currents, but those connected in series would have the same current passing through them.
current=power/120
a. do the math
b. add them
c. Hmmmm.
You ought to do engineering estimates first. 1200w is about 10 amp
1100 watts is about 10 amps
1400 watts is about 10 amps
That answers the last part pretty easily.