A 120-V immersion heater consists of a coil of wire that is...

A $120-\mathrm{V}$ immersion heater consists of a coil of wire that is placed in a cup to boil the water. The heater can boil one cup of $20.00^{\circ} \mathrm{C}$ water in 180.00 seconds. You buy one to use in your dorm room, but you are worried that you will overload the circuit and trip the $15.00-\mathrm{A}$ 120-V circuit breaker, which supplies your dorm room. In your dorm room, you have four $100.00-\mathrm{W}$ incandescent lamps and a $1500.00-\mathrm{W}$ space heater. (a) What is the power rating of the immersion heater? (b) Will it trip the breaker when everything is turned on? (c) If it you replace the incandescent bulbs with 18.00-W LED, will the breaker trip when everything is turned on?

A $120-\mathrm{V}$ immersion heater consists of a coil of wire that is placed in a cup to boil the water. The heater can boil one cup of $20.00^{\circ} \mathrm{C}$ water in 180.00 seconds. You
buy one to use in your dorm room, but you are worried that you will overload the circuit and trip the $15.00-\mathrm{A}$ 120-V circuit breaker, which supplies your dorm room. In your dorm room, you have four $100.00-\mathrm{W}$ incandescent lamps and a $1500.00-\mathrm{W}$ space heater. (a) What is the power rating of the immersion heater? (b) Will it trip the breaker when everything is turned on? (c) If it you replace the incandescent bulbs with 18.00-W LED, will the breaker trip when everything is turned on?

Key Concepts

Energy and Power Relationship

This concept involves understanding that power is the rate at which energy is transferred or converted. In electrical and thermal systems, power is computed as the energy divided by time, which is crucial for determining the energy required to perform tasks (such as heating water) and subsequently finding the power rating of devices. It stems from the basic formula P = E/t.

Specific Heat Capacity and Thermal Energy

Specific heat capacity is a material property that indicates the amount of heat needed to raise the temperature of a unit mass of a substance by one degree Celsius. By using the formula Q = mc?T, where m is the mass, c is the specific heat capacity, and ?T is the temperature change, one can calculate the thermal energy required to heat a substance. This principle is applied when determining the energy needed to heat water in the context of the immersion heater.

Power Rating of Electrical Appliances

The power rating of an appliance, measured in watts, represents the rate at which the appliance consumes energy under normal operating conditions. It provides an indication of how much electrical power is required for its operation. In the context of the problem, calculating the immersion heater's power rating involves relating the electrical energy output needed for heating to the time over which it is applied.

Circuit Load Analysis

Circuit load analysis is the process of summing the power consumption of all devices on a circuit to determine the total current draw, ensuring that it does not exceed the rated capacity of the circuit components, such as a circuit breaker. Understanding how to add individual power ratings and convert the total power to current (using P = VI) is essential for determining if activating all devices simultaneously will trip a circuit breaker.

Circuit Breaker Functionality

A circuit breaker is an electrical safety device designed to protect circuits from overcurrent by interrupting the power supply when the current exceeds a specified limit. This concept is critical when evaluating whether the combined electrical load from multiple devices, including heaters and lighting, will surpass the circuit breaker’s threshold, potentially causing it to trip.

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