AC Circuits
- How is a sinusoidal alternating voltage generated by a coil rotating in a magnetic field? In one line When a coil rotates at constant speed in a uniform magnetic field, the flux linking it changes continuously, so by Faraday's law... 1
- What do cycle, time period, frequency, amplitude and instantaneous value mean for an AC wave? In one line These are the basic terms that describe a repeating AC waveform: how big it gets (amplitude), how long one repetition takes (tim... 1
- What is the RMS value of an alternating current and why is it 0.707 times the peak? In one line The RMS (root mean square) value of an alternating current is the steady DC current that would produce the same heat in a resist... 1
- What is the average value of a sine wave, and how are form factor and peak factor defined? In one line The average value of a sine wave over a half cycle is 2V_m/π ≈ 0.637V_m ; form factor is RMS ÷ average (1.11) and peak factor is... 1
- What is a phasor, and how do you find phase difference between two AC quantities? In one line A phasor is a rotating line whose length represents the RMS (or peak) value of a sinusoid and whose angle represents its phase,... 1
- How do you add or subtract sinusoidal AC quantities using phasors and complex numbers? In one line To add or subtract sinusoids of the same frequency, write each as a phasor in rectangular form (a + jb) , add or subtract the re... 1
- How do current and voltage behave in purely resistive, inductive and capacitive AC circuits? In one line In a pure resistor current is in phase with voltage, in a pure inductor current lags voltage by 90°, and in a pure capacitor cur... 1
- How do you analyse a series RL circuit: impedance, phase angle and power factor? In one line In a series RL circuit the impedance is Z = √(R² + X_L²) , the current lags the voltage by φ = tan⁻¹(X_L/R) , and the power fact... 1
- How do you analyse a series RC circuit and why does its current lead the voltage? In one line In a series RC circuit the impedance is Z = √(R² + X_C²) and the current leads the supply voltage by φ = tan⁻¹(X_C/R) , giving a... 1
- How do you analyse a series RLC circuit and decide if it is inductive or capacitive? In one line In a series RLC circuit Z = √(R² + (X_L - X_C)²) ; if X_L > X_C it behaves inductively (current lags), if X_C > X_L capacitively... 1
- What is admittance, and how is it used to solve parallel AC circuits? In one line Admittance Y = 1/Z measures how easily a branch allows AC to flow; in a parallel circuit, branch admittances simply add, making... 1
- What are real power, reactive power, apparent power and power factor in an AC circuit? In one line Real power P = VIcosφ (W) does useful work, reactive power Q = VIsinφ (VAR) flows back and forth to build magnetic and electric... 1
- What is series resonance in an RLC circuit and what is its resonant frequency? In one line Series resonance occurs at the frequency where X_L = X_C , so the impedance becomes purely resistive and minimum, the current is... 1
- How are three-phase voltages generated and why are they displaced by 120 degrees? In one line Three identical coils placed 120° apart on the same rotor (or stator) of an alternator produce three equal sinusoidal EMFs that... 1
- What is parallel resonance, and how does it differ from series resonance? In one line Parallel resonance occurs in a coil-capacitor parallel (tank) circuit when the reactive currents of the two branches cancel, mak... 1
- What are line and phase voltage and current relations in a balanced star connection? In one line In a balanced star (Y) connection, line voltage is √(3) times phase voltage and leads it by 30°, while line current equals phase... 1
- What are line and phase voltage and current relations in a balanced delta connection? In one line In a balanced delta (Δ) connection, line voltage equals phase voltage, while line current is sqrt3 times phase current and lags... 1
- A coil having a resistance of 10 Ω and an inductance of 40 mH is connected to a 200 V, 50 Hz supply. Calculate the impedance of the coil, current, power factor and power consumed. X_L = 2π fL = 2π×50×0.04 = 12.566\ Ω . Impedance: Z = √(10² + 12.566²) = √(257.91) = 16.06 Ω (= 10 + j12.566 = 16.06∠51.49° Ω). Current: I =... 1
- Write down the relation between line current and phase current, line voltage and phase voltage, power in balanced three phase delta connected balanced load. For a balanced delta (Δ) connected load: Voltage: each phase is connected directly between two lines, so V_L = V_ph. Current: each line curr... 1
- An inductive coil having inductance of 0.04 H and resistance 25 Ω has been connected in series with another inductive coil of inductance 0.2 H and resistance 15 Ω. The whole circuit is powered with 230 V, 50 Hz mains. Calculate the power dissipation… Coil 1: R₁ = 25 Ω, X₁ = 2π(50)(0.04) = 12.566\ Ω . Coil 2: R₂ = 15 Ω, X₂ = 2π(50)(0.2) = 62.832\ Ω . Total: R = 25 + 15 = 40 Ω, X = 12.566 +... 1
- What is the necessary condition for resonance in a series circuit? Derive an expression for resonance frequency. Condition: an R-L-C series circuit is at resonance when the inductive reactance equals the capacitive reactance, X_L = X_C. Then the net rea... 1
- A balanced 3-φ, star connected load consist of three coils each consisting of R = 6 Ω and XL = 8 Ω. Determine the 1) Phase impedance 2) Phase voltage 3) Phase current 4) Line current 5) Power factor when connected across 400 V, 50 Hz supply. Given: star connection, R = 6 Ω, X_L = 8 Ω, V_L = 400 V, 50 Hz. 1) Phase impedance: Z_ph = √(6²+8²) = 10 Ω (= 6 + j8 = 10∠53.13° Ω). 2) Phas... 1
- Find RMS value of current flowing through a 314 μF capacitor when connected to 230 V, 50 Hz, single phase AC supply. Write the equation of instantaneous voltage and current. X_C = 1/2π fC = dfrac12π×50×314×10⁻⁶ = 1/0.09865 = 10.14\ Ω . RMS current: I = V/X_C = 230/10.14 = 22.69 A. V_m = 230√2 = 325.27 V; I_m = 22... 1
- A voltage e(t) = 100 sin 314 t is applied to a series circuit consisting of 10 Ω resistance, 0.0318 H inductance and a capacitor of 63.6 μF. Calculate (i) impedance of a series circuit, (ii) expression for i(t), (iii) power factor (iv) active power,… Given: V_m = 100 V, ω = 314 rad/s (f = 50 Hz), R = 10 Ω, L = 0.0318 H, C = 63.6 μF. X_L = ω L = 314×0.0318 = 9.985\ Ω ≈ 10\ Ω ; X_C = 1/ω C... 1