AC Circuits

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e = e₀ sin ωt Where: • e = instantaneous emf at time t • e₀ = peak value of emf (amplitude) • ω = angular frequency (2πf rad/s) • t = time in seconds The voltage varies sinusoidally with time, changi

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Given: i₀ = 10 A **RMS Value:** iᵣₘₛ = i₀/√2 = 10/√2 = 10/1.414 = 7.07 A **Average Value (over half cycle):** iₐᵥ = 0.637 × i₀ = 0.637 × 10 = 6.37 A Note: Average over complete cycle is zero due to

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**Phasor**: A rotating vector that represents a sinusoidally varying quantity. **Key Features:** • Length = peak value (amplitude) • Rotates counterclockwise at angular frequency ω • Projection on ve

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**Phase Relationship**: Voltage and current are **in phase** (φ = 0°) **Mathematical Expression:** • e = e₀ sin ωt • i = i₀ sin ωt • where i₀ = e₀/R **Reason**: Resistance follows Ohm's law (V = IR)

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**Inductive Reactance (XL)**: Opposition offered by an inductor to AC flow **Formula**: XL = ωL = 2πfL **Given**: L = 0.1 H, f = 50 Hz **Solution**: XL = 2πfL = 2 × 3.14 × 50 × 0.1 XL = 31.4 Ω **K

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**Phase Relationship**: Current **lags** voltage by 90° (π/2 radians) **Mathematical Expression**: • e = e₀ sin ωt • i = i₀ sin(ωt - π/2) • where i₀ = e₀/XL = e₀/(ωL) **Physical Reason**: Self-induc

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**Capacitive Reactance (XC)**: Opposition offered by a capacitor to AC flow **Formula**: XC = 1/(ωC) = 1/(2πfC) **Given**: C = 25 μF = 25 × 10⁻⁶ F, f = 50 Hz **Solution**: XC = 1/(2πfC) = 1/(2 × 3.

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**Phase Relationship**: Current **leads** voltage by 90° (π/2 radians) **Mathematical Expression**: • e = e₀ sin ωt • i = i₀ sin(ωt + π/2) • where i₀ = e₀/XC = e₀ωC **Physical Reason**: Current flow