AC Fundamentals
1. Instantaneous, Peak, RMS, and Average Values
- Instantaneous Value: Value of AC at any given time.
- Peak Value (Vm): Maximum positive or negative value of the waveform.
- RMS Value: Root Mean Square = 0.707 × Vm (useful for power calculation).
- Average Value: 0.637 × Vm for one half-cycle of sine wave.
Vrms = Vm / √2
Vavg = (2Vm) / π
2. Representation of Sinusoidal Wave
- Standard form of sinusoidal voltage: v(t) = Vm sin(ωt + φ)
- Vm = peak voltage, ω = 2πf = angular frequency, φ = phase angle
3. Series & Parallel AC Circuits (R-L, R-C)
- R-L Circuit: Current lags voltage due to inductor.
- R-C Circuit: Current leads voltage due to capacitor.
R-L: Z = √(R² + XL²), where XL = 2πfL
R-C: Z = √(R² + XC²), where XC = 1/(2πfC)
4. Resonance and Tank Circuit
- Resonance: Occurs when XL = XC (inductive and capacitive reactance equal).
- Resonant Frequency: fr = 1 / (2π√LC)
- Tank Circuit: A parallel LC circuit, used in oscillators and filters.
5. Polyphase System – Star and Delta Connection
- Star (Y) Connection: Line voltage = √3 × Phase voltage
- Delta (Δ) Connection: Line voltage = Phase voltage
3-Phase Power (P) = √3 × VL × IL × cos(φ)
6. DC and Sinusoidal Response of R-L & R-C Circuits
- DC Response: Current rises/exponentially decays with time.
- AC Response: Phase shift, impedance changes based on frequency.
R-L (DC): I(t) = (V/R)(1 - e^(-Rt/L))
R-C (DC): Vc(t) = V(1 - e^(-t/RC))
7. Previous Year Questions (SSC JE, RRB, HSSC)
- Q: In an AC circuit, the voltage leads the current by 90°. What is the nature of the circuit?
Ans: Pure Capacitive
- Q: RMS value of sine wave with 100V peak value?
Ans: 70.7V
- Q: For resonance in RLC circuit, which condition is satisfied?
Ans: XL = XC
- Q: In star connection, how is phase voltage related to line voltage?
Ans: Vph = VL / √3