A water heater consisting of a metal coil that is connected...

A water heater consisting of a metal coil that is connected across the terminals of a $15.0-\mathrm{V}$ power supply is able to heat $250 \mathrm{~mL}$ of water from room temperature to boiling point in 45.0 s. What is the resistance of the coil?

Key Concepts

Joule Heating

Joule heating refers to the process by which electric energy is converted into thermal energy in a resistive material. It is governed by the formulas P = I²R or P = V²/R, which relate the power dissipated as heat to the current flowing through and the resistance of the material. This concept is fundamental in understanding how electrical energy is transformed into heat in devices like heating coils.

Electrical Resistance

Electrical resistance is a measure of how strongly a material opposes the flow of electric current. It is a crucial property in circuit analysis because it determines the rate at which electrical energy is converted into heat. The resistance of a component affects how much current can flow for a given applied voltage, according to Ohm’s law.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. This property is essential for calculating the energy needed to heat a substance, as it directly relates the mass of the substance and the desired temperature change to the energy required.

Energy Conversion in Thermal Systems

Energy conversion in thermal systems involves calculating how the electrical energy supplied to a device, such as a heating coil, is transformed into thermal energy that raises the temperature of another substance. This typically involves equating the energy delivered electrically (using power and time) with the energy absorbed thermally (using mass, specific heat capacity, and temperature change).

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