A household branch circuit is protected by a 15A circuit breaker and is supplied at a constant potential difference of 120V. A homeowner wishes to use the branch to power three appliances simultaneously:
• A hair dryer labeled “1.6 kW, 120 V”
• A space heater labeled “1.1 kW, 120 V”
• A desk lamp that contains an LED driver drawing a steady 0.15A from the line
All appliances behave as purely resistive loads at the labeled conditions.
(a) Calculate the current drawn by each appliance when operated separately at 120V.
(b) If all three appliances are plugged into the same branch circuit and turned on simultaneously, determine the total current that would flow through the circuit breaker.
(c) State whether the circuit breaker will trip under the conditions in part (b) and justify your answer quantitatively.
(d) To avoid tripping the breaker while keeping the hair dryer running, the homeowner decides to unplug exactly one of the other two devices. Identify which device should be unplugged to ensure safe operation, and show calculations supporting your choice.
(e) Suppose instead the homeowner replaces the hair dryer with a model labeled “1.2 kW, 120 V.” Discuss how the maximum number of the original three devices could then be operated simultaneously without tripping the breaker, again supporting your answer with numerical evidence.