A 540-W electric heater is designed to operate from 120 V lines. (a) What is its resistance? (b)

step 1 Here we have an electric heater of 540 watt operating at a voltage of 120 volt. So we have power

A 540-W electric heater is designed to operate from 120 V...

A $540-\mathrm{W}$ electric heater is designed to operate from 120 $\mathrm{V}$ lines. (a) What is its resistance? (b) What current does it draw? (c) If the line voltage drops to $110 \mathrm{V},$ what power does the heater take? (Assume that the resistance is constant. Actually, it will change because of the change in temperature.) (d) The heater coils are metallic, so that the resistance of the heater decreases with decreasing temperature. If the change of resistance with temperature is taken into account, will the electrical power consumed by the heater be larger or smaller than what you calculated in part (c)? Explain.

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electricity that describes the linear relationship between voltage, current, and resistance in a circuit. It states that the voltage across a conductor is directly proportional to the current flowing through it, expressed as V = IR, where V is voltage, I is current, and R is resistance.

Electric Power

Electric power is the rate at which electrical energy is consumed or converted into another form of energy in a circuit. It can be defined using the formula P = VI, which relates power to voltage and current. Additionally, by using Ohm's Law, power can be expressed as P = I²R or P = V²/R, allowing for calculations in circuits where resistance or voltage is constant.

Resistance Calculation

Calculating resistance involves determining the opposition to the current flow in a circuit using known values of voltage and power. When a device is rated for a particular power and voltage, its resistance can be derived from the power formulas such as P = V²/R, making it an essential parameter for understanding circuit behavior under different operating conditions.

Temperature Dependence of Resistance

In metallic conductors, resistance typically changes with temperature due to the temperature coefficient of resistance. As the temperature decreases, the atoms vibrate less, usually leading to a decrease in resistance. This concept is critical when analyzing devices like heaters, where the resistance may not remain constant as the operating temperature changes, thereby affecting the actual power consumption compared to calculated values assuming constant resistance.

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