The heating element of an electric oven is designed to produce 3.1 kW of heat when connected to a 240-V source. What must be the resistance of the element?

검증된 단계별 안내

Identify the relationship between power, voltage, and resistance using the formula:

P = V^{2} / R

, where

P

is power,

V

is voltage, and

R

is resistance.

Rearrange the formula to solve for resistance:

R = V^{2} / P

Substitute the given values into the formula:

V = 240 \, V

and

P = 3.1 \, kW = 3100 \, W

Calculate the square of the voltage:

V^{2} = 240^2

Divide the squared voltage by the power to find the resistance:

R = 240^2 / 3100

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주요 개념

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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 electrical circuits and is essential for calculating resistance when voltage and current are known.

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 is calculated using the formula P = V * I, where P is power in watts, V is voltage in volts, and I is current in amperes. Understanding this concept is crucial for determining the resistance of the heating element based on its power rating and the voltage supplied.

Resistance

Resistance (R) is a measure of the opposition to the flow of electric current in a circuit. It is measured in ohms (Ω) and can be calculated using Ohm's Law. In the context of the heating element, knowing the resistance allows us to understand how much current will flow when a specific voltage is applied, which is necessary for ensuring the element operates safely and effectively at its rated power.