AC Circuits
- Three identical coils each [4.2 + j5.6] Ω are connected in star across 415 V, three-phase, 50 Hz, AC supply. Determine (a) the line current (b) the power factor and (c) the total power. Z_ph = 4.2 + j5.6 = √(4.2² + 5.6²)∠tan⁻¹(5.6/4.2) = 7∠53.13^°\ Ω . Star: V_ph = 415/sqrt3 = 239.6 V. (a) Line current: I_L = I_ph = 239.6/7... 1
- Find supply current, current in each branch and total power factor. [Circuit (dark photograph; values partly illegible in the source scan): an AC source marked "~" at the bottom, labelled approximately "230 V, 50 Hz" (first digits unclear), feeds two… Assumed data (values read from the partly illegible figure): V = 230 V, 50 Hz; branch 1: R₁ = 10 Ω, L = 0.12 H; branch 2: R₂ = 10 Ω, C = 60... 1
- Define the following terms in the series RLC resonance circuit (i) Resonance Frequency, (ii) Resonance curve, (iii) Half-power frequencies or Cut-off frequencies, (iv) Bandwidth, (v) Quality factor (i) Resonance frequency f_r: the frequency at which X_L = X_C, so the circuit impedance is purely resistive (Z = R, minimum), current is max... 1
- An alternating current of frequency 50 Hz has a maximum value of 12 A. Find (i) Equation for instantaneous value of current and (ii) Time taken to reach 9.6 A for the first time. Given: f = 50 Hz, I_m = 12 A. ω = 2π f = 100π = 314.16 rad/s. (i) i = I_msinω t ⇒ i = 12sin(314.16 t) A (i.e. 12sin 100π t ). (ii) 9.6 = 12s... 1
- A coil consumes 1 KW power from 50 Hz single phase ac supply and volt-ampere input is 2 KVA. If value of resistance of coil is 10 Ω then find the following parameters with respect to a coil. (i) Value of inductance, (ii) Phase angle, (iii) Power fact… Given: P = 1000 W, S = 2000 VA, R = 10 Ω, f = 50 Hz. Current: P = I²R ⇒ I = √(1000/10) = 10 A. Voltage: V = S/I = 2000/10 = 200 V. (iv) Impe... 1
- Three similar coils each having a resistance of 5 Ω and an inductance of 0.02 H are connected in star to a 440 V, 50 Hz, 3-phase supply. Calculate (i) line current and (ii) active and reactive power Given: R = 5 Ω, L = 0.02 H, star connection, V_L = 440 V, f = 50 Hz. X_L = 2π fL = 2π×50×0.02 = 6.283\ Ω ; Z_ph = √(5²+6.283²) = √(64.48) =... 1
- Two impedances of 12 + j16 Ω and 10 − j20 Ω are connected in parallel across 230 V, 50 Hz, single phase ac supply. Find admittance, current and power factor of each branch. Take V = 230∠0° V. Branch 1: Z₁ = 12 + j16 = 20∠53.13° Ω. Y₁ = 1/Z₁ = 12-j16/12²+16² = 12-j16/400 = 0.03 - j0.04 S = 0.05∠−53.13° S. I₁ = VY... 1
- State the necessary condition for resonance in a series circuit. Compare series and parallel resonance. Condition for series resonance: in an R-L-C series circuit, resonance occurs when the inductive reactance equals the capacitive reactance, X... 1