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

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First, understand the relationship between power, voltage, and resistance. The formula to use here is the power formula: \( P = \frac{V^2}{R} \), where \( P \) is the power, \( V \) is the voltage, and \( R \) is the resistance.

Rearrange the formula to solve for resistance \( R \). This gives us \( R = \frac{V^2}{P} \).

Substitute the given values into the formula. The power \( P \) is 4.1 kW, which is equivalent to 4100 W, and the voltage \( V \) is 240 V.

Calculate \( V^2 \) by squaring the voltage: \( V^2 = 240^2 \).

Finally, divide \( V^2 \) by \( P \) to find the resistance \( R \): \( R = \frac{240^2}{4100} \). This will give you the resistance of the dryer's heating element at its operating temperature.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electric Power

Electric power is the rate at which electrical energy is transferred by an electric circuit. It is measured in watts (W) and calculated using the formula P = VI, where P is power, V is voltage, and I is current. Understanding power is crucial for determining how much energy the dryer uses.

Ohm's Law

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance. It is expressed as V = IR, where V is voltage, I is current, and R is resistance. This law is essential for calculating the resistance of the dryer's heating element.

Resistance

Resistance is a measure of the opposition to the flow of electric current in a circuit. It is measured in ohms (Ω) and affects how much current flows for a given voltage. Calculating the resistance of the dryer's heating element involves using the power and voltage values to find how much the element resists the current flow.

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