Ch 32: AC Circuits

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 32: AC Circuits

문제 67c

32장, 문제 67c

A motor attached to a 120 V/60 Hz power line draws an 8.0 A current. Its average energy dissipation is 800 W. What is the motor's resistance?

검증된 단계별 안내

Step 1: Start by recalling Ohm's Law, which relates voltage (V), current (I), and resistance (R) as:

V = I R

. Rearrange this equation to solve for resistance:

R = V / I

Step 2: Identify the given values from the problem: the voltage

V = 120

V and the current

I = 8.0

Step 3: Substitute the given values into the formula for resistance:

R = \frac{120}{8.0}

. Perform the division to find the resistance.

Step 4: Verify the calculated resistance by checking if it aligns with the power dissipation formula:

P = I R^{2}

. Rearrange to solve for

R

and confirm consistency with the given power

P = 800

Step 5: Conclude by ensuring all units are consistent and the resistance value is reasonable for the given motor's operation.

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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, allowing us to calculate 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 uses energy, calculated using the formula P = V * I, where V is voltage and I is current. In this context, power can also be expressed in terms of resistance using P = I² * R. Understanding this relationship is crucial for analyzing how much energy a device dissipates as heat or performs work.

Resistive Load

A resistive load is an electrical component that consumes power primarily in the form of heat, such as a motor or a resistor. In a resistive load, the current and voltage are in phase, meaning they reach their maximum and minimum values simultaneously. This concept is important for calculating resistance in circuits where the load behaves according to Ohm's Law, allowing for straightforward analysis of energy dissipation.

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