The heating element of a toaster dissipates 1500 W when connected to a 120 V/60 Hz power line. What is its resistance?

검증된 단계별 안내

Start by recalling the formula for electrical power dissipation in terms of voltage and resistance:

P = 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

R = V^{2} / P

Substitute the given values into the formula:

V = 120

volts and

P = 1500

watts.

Square the voltage:

V^{2} = 120^2

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

R = 120^2 / 1500

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 helps in calculating resistance when voltage and current are known.

Power in Electrical Circuits

The power (P) dissipated in an electrical circuit is the rate at which energy is used or converted and is calculated using the formula P = V * I, where V is voltage and I is current. In the context of resistive devices like a toaster, power can also be expressed as P = I^2 * R or P = V^2 / R, allowing for the calculation of resistance when power and voltage are known.

Resistance

Resistance (R) is a measure of the opposition to the flow of electric current in a conductor. It is measured in ohms (Ω) and depends on the material, length, and cross-sectional area of the conductor. In the context of the toaster, calculating resistance is essential to understand how efficiently it converts electrical energy into heat, which is crucial for its operation.