What is an AC Circuit?
An AC (alternating current) circuit is driven by a voltage source that periodically reverses direction, tracing a sine wave over time. It powers everything from household outlets to audio amplifiers and motors.
An AC circuit carries current that alternates direction periodically, described by v(t) = Vmax·sin(ωt), unlike DC which flows in one constant direction.
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Step-by-step worked examples
A US household outlet reads 120 V RMS. Find the peak voltage.
Vrms = Vmax/√2, so Vmax = Vrms×√2 Vmax = 120 × 1.4142 = 169.7 V
European mains runs at f = 50 Hz. Find the angular frequency ω and period T.
ω = 2πf = 2π×50 = 314.16 rad/s T = 1/f = 1/50 = 0.02 s = 20 ms
Given v(t) = 170·sin(377t), find the voltage at t = 2 ms.
ωt = 377 × 0.002 = 0.754 rad sin(0.754 rad) ≈ 0.685 v = 170 × 0.685 ≈ 116.4 V
Flashcards
Quick quiz
Q1.In an AC circuit, the current:
Q2.Standard mains frequency in the United States is:
Q3.How does the RMS voltage relate to the peak voltage?
Q4.Angular frequency ω equals:
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Common mistakes
Thinking AC voltage never changes sign. — Correct: AC voltage reverses polarity every half-cycle by definition.
Using the peak value to calculate real power. — Correct: Use the RMS value: P = Vrms²/R for average AC power.
Confusing frequency f with angular frequency ω. — Correct: They're related by ω = 2πf but have different units (Hz vs rad/s).
Assuming AC only exists at 50 Hz or 60 Hz. — Correct: AC can be any frequency — audio signals, radio waves and more are all AC.
FAQ
What is an AC circuit?
An AC circuit is a circuit driven by an alternating voltage or current source that periodically reverses direction, unlike DC.
What is the formula for AC voltage?
The instantaneous voltage is v(t) = Vmax·sin(ωt), where ω = 2πf.
What are examples of AC circuits?
Household wiring, transformers, audio amplifiers and power grids all use AC circuits.
How do you calculate RMS voltage in an AC circuit?
Divide the peak voltage by √2: Vrms = Vmax/√2 ≈ 0.707×Vmax.