Chapter summary — Alternating Current
Alternating current (AC) varies sinusoidally with time: i(t)=I_0 sin(ωt+φ). Key quantities: peak (I_0), RMS value (I_rms = I_0/√2), angular frequency ω=2πf, period T=1/f. In AC circuits, reactances of inductor and capacitor are X_L=ωL and X_C=1/(ωC). Impedance Z generalises resistance: for series R-L-C, Z=√(R^2+(X_L−X_C)^2). Phase difference between voltage and current depends on reactance: current lags voltage in inductive circuits and leads in capacitive circuits. Resonance occurs when X_L=X_C ⇒ ω_0=1/√(LC), giving maximum current in series resonance and minimum impedance in series RLC. Power in AC: instantaneous p(t)=v(t)i(t), average (real) power P=V_rms I_rms cosφ, reactive power Q=V_rms I_rms sinφ, apparent power S=V_rms I_rms. Power factor cosφ important for efficiency; can be corrected using capacitors/inductors. Quality factor Q=ω0L/R (series) measures sharpness of resonance. Transformers, AC generators, and practical aspects like measurement (oscilloscope, multimeter) and safety are also important.
Revision tips: Memorize RMS relations, X_L and X_C formulas, resonance condition, power formulas, and practice phasor diagrams and circuit calculations at resonance and off-resonance.
1. The RMS value of a sinusoidal current I(t)=I_0 sin(ωt) is:
A) I_0
B) I_0/√2 ✅
C) I_0/2
D) 2I_0
2. The average value of a pure sinusoidal current over one complete cycle is:
A) Zero ✅
B) I_0
C) I_rms
D) I_0/2
3. For an inductor of inductance L in AC circuit, reactance X_L is:
A) 1/(ωL)
B) ωL ✅
C) R
D) ω/C
4. For a capacitor of capacitance C in AC circuit, reactance X_C is:
A) 1/(ωC) ✅
B) ωC
C) ωL
D) R
5. In an AC circuit if current lags the voltage by 90°, the circuit is:
A) Purely capacitive
B) Purely inductive ✅
C) Purely resistive
D) Resonant
6. In a purely resistive AC circuit, the phase difference between current and voltage is:
A) 90°
B) 0° ✅
C) 45°
D) 180°
7. Impedance Z of a series R-L-C circuit is:
A) R + j(X_L + X_C)
B) √(R^2 + (X_L − X_C)^2) ✅
C) 1/√(R^2 + (XL − XC)^2)
D) R·(X_L − X_C)
8. Resonance in a series RLC circuit occurs when:
A) X_L = 0
B) X_L = X_C ✅
C) R = 0
D) ω = 0
9. Resonant angular frequency ω_0 for an LC circuit is:
A) 1/LC
B) √(L/C)
C) 1/√(LC) ✅
D) √(C/L)
10. At resonance in a series RLC circuit, the current is:
A) Minimum
B) Maximum ✅
C) Zero
D) Infinite always
11. Quality factor Q of a series RLC circuit is defined as:
A) ω_0 L / R ✅
B) R / ω_0 L
C) ω_0 C / R
D) R C
12. In a series resonant circuit, at resonance the impedance equals:
A) R ✅
B) X_L
C) X_C
D) 0
13. The apparent power S in an AC circuit is given by:
A) V_rms I_rms ✅
B) V_rms I_rms cosφ
C) V_rms I_rms sinφ
D) V_peak I_peak
14. Power factor is defined as:
A) sinφ
B) cosφ (ratio of real power to apparent power) ✅
C) tanφ
D) cotφ
15. Reactive power Q is given by:
A) V_rms I_rms cosφ
B) V_rms I_rms sinφ ✅
C) V_rms I_rms
D) V_rms^2 / R
16. In a purely capacitive circuit the current _____ the voltage by 90°.
A) Lags
B) Leads ✅
C) Is in phase
D) Is zero
17. The impedance of a capacitor in complex form is:
A) jωC
B) −j/(ωC) ✅
C) 1/jωC
D) R + jX
18. The phasor representation helps to convert _____ problems into algebraic ones.
A) Thermal
B) AC circuit (sinusoidal) ✅
C) DC circuit
D) Mechanical
19. The power dissipated in a pure inductor over one complete AC cycle is:
A) Positive
B) Zero (energy returned to source) ✅
C) Negative
D) Infinite
20. The average power in an AC circuit containing resistance R and reactance X is:
A) V_rms^2 / Z
B) V_rms I_rms cosφ ✅
C) V_peak I_peak
D) V_rms I_rms sinφ
21. For a series RLC circuit, phase angle φ between source voltage and current is given by:
A) tanφ = (X_L − X_C)/R ✅
B) tanφ = R/(X_L − X_C)
C) tanφ = X_C / X_L
D) tanφ = 0
22. At resonance in a parallel RLC circuit, the impedance is:
A) Maximum ✅
B) Minimum
C) Zero
D) Equal to R
23. In AC, the effective value of a sinusoidal voltage is equal to:
A) Peak value
B) Peak value/√2 ✅
C) Average value
D) Twice the peak
24. The impedance of a series RL circuit is Z = √(R^2 + (ωL)^2). If ω increases, Z:
A) Decreases
B) Increases ✅
C) Remains same
D) Goes to zero
25. In an LCR series circuit, bandwidth Δω = ω_0/Q. Higher Q means:
A) Wider bandwidth
B) Narrower bandwidth (sharper resonance) ✅
C) Lower peak current
D) No resonance
26. The phase difference between current and voltage in a series circuit at resonance is:
A) 90°
B) 0° ✅
C) −90°
D) 180°
27. A wattmeter measures:
A) Apparent power
B) Reactive power
C) Real power (average power) ✅
D) RMS voltage only
28. Power factor correction is usually achieved by adding:
A) Resistors
B) Inductors
C) Capacitors (to compensate inductive load) ✅
D) More generators
29. The instantaneous power p(t) in AC circuit with v=V_peak sinωt and i=I_peak sin(ωt+φ) is:
A) Product of instantaneous v and i (p(t)=v(t)i(t)) ✅
B) V_peak I_peak only
C) Constant
D) Zero always
30. In AC circuits, a current phasor is represented as:
A) Vector in complex plane ✅
B) Scalar only
C) Real number only
D) Matrix
31. If X_L > X_C in a series RLC circuit, the circuit is _____ and current _____ voltage.
A) Inductive; lags ✅
B) Capacitive; leads
C) Resistive; in phase
D) Resonant; in phase
32. For a capacitor, increasing frequency results in _____ reactance.
A) Increased
B) Decreased (X_C = 1/ωC) ✅
C) No change
D) Infinite
33. The phasor diagram for a purely inductive circuit shows current _____ voltage by 90°.
A) Leading
B) Lagging ✅
C) In phase
D) Opposite
34. An AC source V=V_0 sin(ωt) connected to capacitor C. The charge on capacitor is q(t)=C V_0 sin(ωt). The current is:
A) i(t)=C V_0 ω cos(ωt)
B) i(t)=C V_0 ω cos(ωt) ✅
C) i(t)=V_0 / C
D) i(t)=0
35. The peak-to-peak value of a sinusoidal voltage is equal to:
A) 2 V_peak ✅
B) V_peak/2
C) V_rms
D) V_peak
36. A series resonant circuit is used as a:
A) Band-pass filter ✅
B) Band-stop filter
C) Low-pass filter
D) High-pass filter
37. In power triangle, the vertical component represents _____ and horizontal represents _____.
A) Real, Reactive
B) Reactive (Q), Real (P) ✅
C) Apparent and Real
D) Voltage and Current
38. Phase angle φ in AC circuits is given by φ = _____ between voltage and current.
A) Magnitude only
B) Phase difference ✅
C) Frequency difference
D) Time constant
39. In an AC circuit, if V_rms = 230 V and I_rms = 10 A and cosφ = 0.8, real power is:
A) 2300 W
B) 1840 W (P=VIcosφ) ✅
C) 23000 W
D) 92 W
40. The impedance of a series RC circuit at high frequencies tends to:
A) Infinity
B) R (capacitor shorted at high freq) ✅
C) Zero
D) 1/(ωC)
41. In AC, capacitive reactance X_C _____ with frequency and inductive reactance X_L _____ with frequency.
A) Increases; decreases
B) Decreases; increases ✅
C) Both increase
D) Both decrease
42. An oscilloscope displays AC waveforms in _____ domain.
A) Time domain ✅
B) Frequency domain
C) Phase domain
D) Complex domain
43. In a three-phase power system, phase difference between phases is:
A) 60°
B) 120° ✅
C) 90°
D) 180°
44. For a parallel resonant circuit (tank), the circuit behaves as _____ near resonance.
A) Low impedance
B) High impedance (parallel resonance) ✅
C) Short circuit
D) Resistive only
45. The phasor addition of two sinusoidal voltages of same frequency is equivalent to:
A) Vector addition of phasors ✅
B) Scalar algebraic addition
C) Multiplication
D) Division
46. In AC, the term 'crest factor' refers to:
A) Ratio of peak value to RMS value ✅
B) Ratio of RMS to average
C) Phase angle
D) Frequency
47. The instantaneous voltage across an inductor is v=L di/dt. For sinusoidal current i=I_0 sinωt, v is:
A) L I_0 ω cosωt ✅
B) L I_0 sinωt
C) Zero
D) L I_0 / ω
48. The maximum energy stored alternately in capacitor and inductor in LC circuit equals:
A) ½ C V_0^2 = ½ L I_0^2 ✅
B) C V_0
C) L I_0
D) Zero
49. In an AC circuit, apparent power S = 1000 VA and real power P = 800 W. Power factor is:
A) 0.8 ✅
B) 1.25
C) 0.5
D) 800
50. Which device converts AC to DC?
A) Transformer
B) Rectifier ✅
C) Inverter
D) Alternator