The heating element of an electric dryer is rated at 4.1 kW when connected to a 240-V line. (b) What is the resistance of the dryer's heating element at its operating temperature?

Verified step by step guidance

1. Identify the power (P) and the voltage (V) given in the problem. Here, P = 4.1 kW and V = 240 V.
2. Convert the power from kilowatts to watts for ease of calculation. Recall that 1 kW = 1000 W, so multiply 4.1 kW by 1000.
3. Use the formula for power in terms of resistance and voltage, which is P = V^2 / R, where R is the resistance.
4. Rearrange the formula to solve for the resistance R. The formula becomes R = V^2 / P.
5. Substitute the values of V and P into the rearranged formula to find the resistance R of the dryer's heating element.

Key Concepts

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. It is mathematically expressed as V = I * R. This relationship is fundamental in understanding how electrical components behave in a circuit.

Power in Electrical Circuits

The power (P) consumed by an electrical device is defined as the rate at which it converts electrical energy into another form of energy, such as heat. It can be calculated using the formula P = V * I, where V is voltage and I is current. In this context, knowing the power rating of the heating element allows us to relate it to the voltage and resistance.

Resistance Calculation

Resistance (R) is a measure of the opposition to the flow of electric current in a circuit. It can be calculated using the rearranged form of Ohm's Law: R = V / I. In the case of the dryer, once the current is determined from the power and voltage, the resistance can be easily calculated, providing insight into the heating element's efficiency and performance.