Ch 32: AC Circuits

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo

Knight Calc 5th Edition

Ch 32: AC Circuits

Problema 36

Capitolo 32, Problema 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?

Guida verificata passo dopo passo

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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Concetti chiave

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

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Resistance and Ohm's Law

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.

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Power in Circuits

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.

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Root-Mean-Square Speed of Ideal Gases

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