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 36

32장, 문제 36

A resistor dissipates 2.0 W when the rms voltage of the emf is 10.0 V. At what rms voltage will the resistor dissipate 10.0 W?

검증된 단계별 안내

Step 1: Recall the formula for power dissipated in a resistor:

P = V^{2} / R

, where

P

is the power,

V

is the rms voltage, and

R

is the resistance.

Step 2: Use the given data for the first case to calculate the resistance of the resistor. Rearrange the formula to solve for

R

R = V^{2} / P

. Substitute

V = 10.0

V and

P = 2.0

Step 3: Once the resistance

R

is determined, use the same power formula for the second case where the power is 10.0 W. Rearrange the formula to solve for the new rms voltage

V

V = \sqrt{P \cdot R}

Step 4: Substitute the value of

R

(calculated in Step 2) and

P = 10.0

W into the formula to find the new rms voltage.

Step 5: Simplify the expression to determine the new rms voltage. This will give the voltage at which the resistor dissipates 10.0 W.

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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 = IR. This relationship is fundamental in understanding how voltage, current, and resistance interact in electrical circuits.

Power in Electrical Circuits

The power (P) dissipated by a resistor in an electrical circuit is given by the formula P = V^2 / R, where V is the voltage across the resistor and R is its resistance. This formula indicates that power is proportional to the square of the voltage, meaning that if the voltage increases, the power dissipated increases significantly, assuming resistance remains constant.

Root Mean Square (RMS) Voltage

RMS voltage is a statistical measure of the magnitude of a varying voltage. It represents the equivalent direct current (DC) voltage that would produce the same power dissipation in a resistor as the alternating current (AC) voltage does. For sinusoidal voltages, the RMS value is calculated as V_rms = V_peak / √2, which is crucial for analyzing AC circuits and understanding power dissipation.