Ch 31: Alternating Current

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo

Young & Freedman Calc 15th Edition

Ch 31: Alternating Current

Problema 12a

Capitolo 31, Problema 12a

You have a 200-Ω resistor, a 0.400-H inductor, and a 6.00-μF capacitor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has voltage amplitude 30.0 V and an angular frequency of 250 rad/s. What is the impedance of the circuit?

Guida verificata passo dopo passo

Start by understanding the concept of impedance in an RLC circuit. Impedance is the total opposition that a circuit presents to the flow of alternating current (AC) and is a combination of resistance (R), inductive reactance (X_L), and capacitive reactance (X_C). In a series RLC circuit, impedance (Z) is given by the formula:

Z = \sqrt{R^{2} + (X^{L} - X^{C}) 2}

Calculate the inductive reactance (X_L) using the formula:

X L_{=} ω L

, where

ω

is the angular frequency and

L

is the inductance. Substitute the given values:

ω = 250

rad/s and

L = 0.400

Calculate the capacitive reactance (X_C) using the formula:

X C_{=} \frac{1}{ω C}

, where

C

is the capacitance. Substitute the given values:

C = 6.00 \times 10 - 6

Substitute the calculated values of X_L and X_C into the impedance formula:

Z = \sqrt{200^{2} + (X L_{-} X C) 2}

Finally, simplify the expression to find the impedance Z. Remember that impedance is a complex quantity, but in this case, you are finding its magnitude, which is a real number.

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Impedance in AC Circuits

Impedance is the total opposition a circuit offers to the flow of alternating current (AC) and is a combination of resistance and reactance. In a series RLC circuit, impedance (Z) is calculated using Z = √(R² + (X_L - X_C)²), where R is resistance, X_L is inductive reactance, and X_C is capacitive reactance.

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Percorso guidato

08:40

Impedance in AC Circuits

Inductive Reactance

Inductive reactance (X_L) is the opposition to the change in current by an inductor in an AC circuit. It is given by X_L = ωL, where ω is the angular frequency and L is the inductance. It increases with frequency, causing a phase shift between voltage and current.

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Percorso guidato

12:59

Mutual Induction

Angular Frequency

Angular frequency (ω) is a measure of how quickly the AC voltage oscillates, expressed in radians per second. It is related to the frequency (f) by ω = 2πf. Angular frequency is crucial for calculating reactance and impedance in AC circuits, affecting how components like inductors and capacitors behave.

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Percorso guidato

05:08

Circumference, Period, and Frequency in UCM

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