Electrical Engineering UPSC PYQ 2024

a) (i) An AM signal s(t) = A_c[1 + k_a m(t)] cos(2π f_c t) is applied to the system shown. Show that the message signal m(t) can be obtained from the square-rooter output v₃(t). Assume |k_a m(t)| < 1 for all t, that m(t) is limited to –ω_s ≤ f ≤ ω_s and that the carrier frequency f_c > 2ω_s. (ii) A narrow-band FM signal is approximately given as s(t) = A_c cos(2π f_c t) – βA_c sin(2π f_c t) sin(2π f_m t). Determine the envelope of this modulated signal. Also determine the ratio of the maximum to the minimum value of this envelope. Plot this ratio versus β for 0 ≤ β ≤ 0·4. Also determine the average power of the narrow-band FM signal as a percentage of the average power of the unmodulated carrier. b) (i) Explain why PWM inverters are preferred over square-wave inverters. Further, draw the harmonic spectrum to highlight differences between unipolar and bipolar PWM techniques. (ii) A single-phase, full-bridge inverter has a DC-link voltage V_DC = 400 V and fundamental frequency 50 Hz. Find the r.m.s. value of the voltages of the fundamental and the next two prominent harmonics for : (1) square-wave mode, and (2) voltage-cancellation mode with α = 20°.3a:["$","div","MAINS_2024_E Show extraction of m(t) from square-rooter output for the given AM signal and assumptions. [10M] For the narrow-band FM signal, find the envelope, ratio of max/min envelope, plot versus β (0–0·4), and compute average power percentage. [10M] Explain preference for PWM inverters over square-wave; draw harmonic spectrum for unipolar and bipolar PWM. [10M] For a single-phase full-bridge inverter (V_DC = 400 V, 50 Hz), find r.m.s. fundamental and next two harmonic voltages for (1) square-wave mode, (2) cancellation mode with α = 20°. [10M] <!--qid:MAINS_2024_Electrical_Engineering-I_Q6-->

(a) In the figure shown, the plane y + z = 1 divides space into region 1 (containing the origin) with μ_r1 = 5 and region 2 with μ_r2 = 7. Given B̅_1 = 3.0 a_x + 1.0 a_y (T), determine B̅_2 and H̅_2. Take μ_0 = 4π×10^-7 H/m. (b) The message signal m(t) has a bandwidth of 20 kHz, a power of 20 W and a maximum amplitude of 8. It is to be transmitted to a destination through a channel having 80 dB attenuation and additive white noise with power spectral density S_n(f) = N_0/2 = 0.5×10^-12 W/Hz. An SNR of at least 50 dB is required at the modulator output. Determine the required transmitter power and channel bandwidth for each of the following schemes: (i) DSB-SC AM (ii) SSB AM (iii) Conventional DSB AM with modulation index 0.6 (c) An ideal DC–DC converter (shown) has V_s = 20 V, duty ratio D = 0.25 and switching frequency 20 kHz. With L = 150 µH, C = 240 µF and average diode current 1.2 A, calculate: (i) Peak-to-peak inductor ripple current (ii) Peak current through switch S <!--qid:MAINS_2024_Electrical_Engineering-I_Q8-->

(a) What are the limitations of (i) Proportional (P), (ii) Integral (I), (iii) Derivative (D), and (iv) PID Controllers? What is the application of positive feedback control system? (b) Explain the operation performed by 8085 microprocessor when the following arithmetic instructions are executed: (i) ADD M (ii) ADC M (iii) DAD rp (iv) SBI d8 (v) DCR reg (c) The ohmmeter circuit has VB = 1.5 V, R1 = 15 kΩ, Rm = 50 Ω, R2 = 50 Ω and meter FSD = 50 μA. Determine the ohmmeter scale reading at 0.5 FSD. (d) Calculate the power loss in a cable insulation having capacitance 9 μF, loss angle 0.05 degree and operating at 11 kV, 50 Hz. Draw the phasor diagram and equivalent circuit also. (e) Explain the concept of a constellation diagram. Draw the PSK signal constellations for the value of M = 2, 4 and 8, if all have same transmitted signal energy Es. <!--qid:MAINS_2024_Electrical_Engineering-II_Q1-->

(c) Find the logic equations for the outputs in the concise form and write the corresponding truth table for the circuit given below : <!--qid:MAINS_2024_Electrical_Engineering-I_Q3-->

(a) (i) Draw the neat and properly labelled output voltage waveform of a three-phase, phase-controlled rectifier having firing angle α. Also derive the relationship for average output voltage in terms of line voltage V_LL and firing angle α. (ii) A three-phase full-wave controlled rectifier is being operated from a star-connected, 415 V, 50 Hz supply. This rectifier is feeding a constant load current of 15 kW. It is required to obtain an average output voltage of 80% of maximum possible output voltage. Find the firing angle, r.m.s. value of line current and input power factor. Assume devices are ideal. (b) (i) Show that the maximum power that a synchronous generator can supply when connected to constant voltage, constant frequency busbars increases with the excitation. (ii) An 11 kV, 3-phase, star-connected turbo-alternator delivers 250 A at unity power factor when running on constant voltage and frequency busbars. If the excitation is increased so that the delivered current rises to 300 A, find the power factor at which the machine now operates and the percentage increase in the induced e.m.f., assuming a constant steam supply and unchanged efficiency. The armature resistance is 0·5 Ω per phase and the synchronous reactance is 10 Ω per phase. (c) A medium has infinite conductivity for z ≤ 0, ε_r = 7 and μ_r = 18, and σ = 0 for z > 0. The electric field for z > 0 is given as E̅ = 10 cos(3×10^8 t − 15x) ẑ. Determine the surface charge density and surface current density at location (3, 4, 0) at t = 0·8 ns. Given, μ_0 = 4π×10^−7 H/m, ε_0 = 1/(36π)×10^−9 F/m.3c:["$","div","MAINS_2024_E <!--qid:MAINS_2024_Electrical_Engineering-I_Q7-->

Answer any or all of the following sub-parts (a) to (e). <!--qid:MAINS_2024_Electrical_Engineering-II_Q5-->

a) In the circuit diagram given here, load resistance R_L is to be set for maximum power transfer. Draw Thevenin equivalent circuit across ab and calculate the value of R_L for maximum power transfer. Also calculate the power loss in resistance R_3, when the circuit is delivering maximum power to load R_L. b) (i) Define input bias current and input offset voltage for an OPAMP. Using an OPAMP, draw an inverting amplifier circuit with gain = –4 in such a way that the effect of bias current is minimized. (ii) In the linear regulated power-supply circuit shown here, calculate the output-voltage adjustment range and maximum power dissipation in transistor T₁ in the worst case. c) A circuit using three 2-input multiplexers is shown below. Determine the function performed by this circuit : Define input bias current and input offset voltage of an OPAMP; draw an inverting amplifier of gain –4 with minimized bias-current effect. [10M] For the given linear regulated power-supply circuit, find the output-voltage adjustment range and the maximum power dissipation in T₁ (worst case). [10M] <!--qid:MAINS_2024_Electrical_Engineering-I_Q4-->

(a) An under-damped second-order system having the transfer function M(s) = K ωn² / ( s² + 2 ξ ωn s + ωn² ) has a frequency-response plot as shown in the figure. Compute the system gain K and the damping factor ξ. (b) A CRT has an anode voltage of 3 kV and its parallel deflecting plates are 2.5 cm long and 5 mm apart. The screen is 30 cm from the centre of the plates. Assuming the amplifier gain applied to the plates is 100, calculate: (i) Beam speed (ii) Deflection sensitivity of the CRT (iii) Deflection factor of the CRT (iv) Input voltage required to deflect the beam through 5 cm (c) Write an assembly-language program to add two numbers of 8-bit data stored in memory locations 4200H and 4201H and store the result in 4202H and 4203H. <!--qid:MAINS_2024_Electrical_Engineering-II_Q3-->

(a) A piezoelectric (low-voltage) transducer has capacitance 2000 pF and charge sensitivity 30 × 10^–3 C/m. Assume a 1 MΩ feedback resistor with 100 pF shunt capacitance for the charge amplifier and a connecting cable of capacitance 150 pF. Calculate: (i) Sensitivity of the cable–transducer combination (ii) High-frequency sensitivity of the complete system (iii) Maximum frequency measurable by the system with ±5 % amplitude error (iv) Value of feedback resistance that can be increased by 5 % error allowance up to 20 kHz <!--qid:MAINS_2024_Electrical_Engineering-II_Q4-->

Answer the following sub-parts (a) and (b). <!--qid:MAINS_2024_Electrical_Engineering-II_Q6-->

a) A uniform plane wave travels in vacuum along +y direction. The electric field of the wave at some instant is given as \vec{E} = 4\hat{x} + 3\hat{z}. Find the vector magnetic field \vec{H}. (Given, μ₀ = 4π×10⁻⁷ H/m, ε₀ = 1/(36π)×10⁻⁹ F/m) b) The maximum efficiency of a 200 kVA, 3300/600 V, 50 Hz, single-phase transformer is 98% and occurs at 75% full load and unity power factor. If the leakage impedance is 10%, find the voltage regulation at full load and power factor 0·8 lagging. c) A diode circuit with an L–C load is shown in the figure, with the capacitor having an initial voltage V_C(t = 0) = 120 V, capacitance C = 12 µF and inductance L = 48 µH. If switch S is closed at t = 0 s, then find : (i) Peak value of current i, and (ii) Conduction time of the diode. d) How can linear pre-emphasis and de-emphasis filters be employed to improve the performance of an FM system? Is the improvement in output S/N ratio dependent on both the frequency responses of the pre-emphasis filter and the de-emphasis filter? e) A transmission line is 25 m long. Its characteristic impedance is Z₀ = 40 Ω and it operates at 2 MHz. The line is terminated with a load of Z_L = (50 + j30) Ω. If the wave velocity is u = 0·8c (with c = 3×10⁸ m/s) on the line, determine (i) the reflection coefficient and (ii) the input impedance.38:["$","div","MAINS_2024_Elect <!--qid:MAINS_2024_Electrical_Engineering-I_Q5-->

(a) The open-loop transfer function of a feedback control system incorporating a dead-time element is given by G(s) = K e^{–Ts} / [ s (s + 1) ] where K > 0 and T > 0 are variable scalar parameters. For a given value of T, show that the closed-loop system will be stable for all values K < K0 where K0 = ω0 cosec (ω0 T), and ω0 is the smallest value of ω satisfying ω = cot (ω T). (b) (i) Compare I/O-mapped I/O and memory-mapped I/O interfacing techniques used in 8085 micro-processor. (ii) What are the operating modes of Port-A of 8255? Explain hand-shake operation in I/O ports. (c) In a parallel circuit, in one branch the current I1 = (100 ± 2) A and in the other branch the current I2 = (200 ± 5) A. Determine the total current considering the following errors: (i) Limiting error (ii) Probable error Comment upon the results as well. <!--qid:MAINS_2024_Electrical_Engineering-II_Q2-->