UPSC Civil Services (Main) Examination 2026 — Electrical Engineering Optional Paper II: Question Paper

09 Sep UPSC Civil Services (Main) Examination 2026 — Electrical Engineering Optional Paper II: Question Paper | Plutus IAS

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The questions below are from Electrical Engineering Optional Paper II of UPSC Civil Services (Main) Examination 2026 (held 2026-08-30) — the actual paper, which is public government content. This page carries the questions for reference and revision; model answers for this paper are not published here.

Official paper (PDF): upsc.gov.in.

(a) A unity feedback system has open loop transfer function $G(s) = \frac{K}{s(s+q)}$. Evaluate the value of K and q so that settling time and peak overshoot will be 6 seconds and 20% respectively. (b) | MVI | B, 0FH | | — | — | | MVI | C, ABH | | MOV | A, C | | ADD | B | | SBI | 02H | | STA | 00FFH | Upon execution of the following routine, find the value stored at location 00FFH. | MVI | B, 0FH | | — | — | | MVI | C, ABH | | MOV | A, C | | ADD | B | | SBI | 02H | | STA | 00FFH | Also write the status of each flag after completion of execution. (c) To evaluate the value of resistance, the voltmeter and ammeter methods are used. The voltmeter reads $500\text{ V}$ with a probable error of $\pm 20\text{ V}$ and the ammeter reads $15\text{ A}$ with probable error of $\pm 3\text{ A}$. Find out the probable error in the computed value of resistance. (d) Discuss the saturated-reactor compensator with the help of circuit diagram and V-I characteristics. How can a lower slope of V-I characteristics be obtained? Also write the main features of the saturated-reactor compensator. (e) $$[P(Y|X)] = \begin{bmatrix} 1-p & p & 0 \\ 0 & p & 1-p \end{bmatrix}$$ A discrete memoryless channel has the following channel matrix : $$[P(Y|X)] = \begin{bmatrix} 1-p & p & 0 \\ 0 & p & 1-p \end{bmatrix}$$ – (i) Draw the channel diagram. – (ii) If the source has equally likely outputs, compute the probabilities associated with the channel output for $p = 0.2$. $5+5=10$ READY READY
(a) ![img-0.jpeg](img-0.jpeg) Determine the response of the system shown in the following figure when it is excited by a unit step input. ![img-1.jpeg](img-1.jpeg) (b) SID SID
SOD SOD (a) A system has a unit response as c(t) = 1 – e^- 0.5t. Evaluate its unit impulse and unit ramp response, assuming zero initial conditions. $$\left[ \begin{array}{l} \dot{x}_1 \\ \dot{x}_2 \end{array} \right] = \left[ \begin{array}{cc} 0 & 1 \\ -1 & -2 \end{array} \right] \left[ \begin{array}{l} x_1 \\ x_2 \end{array} \right]$$ A linear time-invariant system is characterized by the homogeneous state equation. $$\left[ \begin{array}{l} \dot{x}_1 \\ \dot{x}_2 \end{array} \right] = \left[ \begin{array}{cc} 0 & 1 \\ -1 & -2 \end{array} \right] \left[ \begin{array}{l} x_1 \\ x_2 \end{array} \right]$$ Evaluate the solution of the homogeneous equation assuming the initial state vector as x(0) = [1, 0]. (b) An electrodynamometer wattmeter is used for power measurement in a 1-φ circuit. The load voltage is 200 V and load current is 20 A at power factor of 0.5 lagging. The wattmeter voltage circuit has a resistance of 5000 Ω and inductance of 60 mH. Compute the percentage error in the wattmeter reading when pressure coil is connected on the load side. Given that the current coil resistance is 0.4 Ω, inductance is negligible and frequency is 50 Hz. Comment on the result. (c) What are the types of interrupts available in the 8085 microprocessor ? Discuss the use of the EI and DI instructions. Give the significance of each bit of the accumulator when interpreted for the SIM and RIM instructions.
INTR INTR Design a PI controller so that a unity feedback system having open loop transfer function $G(s)H(s) = \frac{10}{(s+2)(s+3)}$ will have the damping ratio of 0.6 and natural frequency of oscillations will be 4 rad/sec. Also determine the characteristic equation of this controller. (b) Write an assembly language program for the 8253/8254 (programmable interval timer) to operate in mode 3 and mode 2. Use counter 0 for which control word register address is 2DH and counter 0 address is 2BH. Input clock is 1 MHz and output frequency is 1 kHz. Design a hardware scheme to interface 8255 (programmable peripheral interface) with 8085, and configure its Port 'A' and Port 'C' as input ports and Port 'B' as output port. Write an assembly language program to take two different numbers from Port 'A' and Port 'C' and display the summation of these numbers on Port 'B' as output. Assume the port addresses are : Port A = 00H Port B = 01H Port C = 02H Control word register address : 03H. (c) A thermistor has a resistance of $4290 \Omega$ at ice point and $980 \Omega$ at $60^{\circ}\text{C}$ . The temperature-resistance relationship is given by $R_T = pR_0 e^{b/T}$ . Evaluate the constants $p$ and $b$ . Also calculate the range of resistance to be measured if the temperature varies from $70^{\circ}\text{C}$ to $120^{\circ}\text{C}$ .
CLK (OUT) In the 8085 microprocessor, explain the functionality of the following pins, and describe the role of the instruction decoder, stack pointer and program counter. CLK (OUT) For the instruction MVI B, 05H, draw the timing diagram, if the opcode is stored at 220AH and data at 220BH locations. Incorporate all the control and status signals involved in the operation during the execution. Assume the opcode is XXH. (c) ![img-2.jpeg](img-2.jpeg) The following circuit is given for the measurement of voltage across a 150 kΩ resistor as shown in the figure. Two voltmeters whose sensitivities are 2000 Ω/V and 30,000 Ω/V respectively are used one by one for this purpose. Both voltmeters have a range of 0 – 100 V. Calculate the reading of each voltmeter. ![img-3.jpeg](img-3.jpeg) (a) ![img-4.jpeg](img-4.jpeg) Write the state space equation for the following circuit. ![img-5.jpeg](img-5.jpeg) (b) A 1 V signal with a source resistance of $R_s = 600 \ \Omega$ is connected to an oscilloscope which has an input impedance of $R_i = 1 \text{ M}\Omega$ in parallel with $C_i = 30 \text{ pF}$. The coaxial cable has a capacitance $C_{cc} = 100 \text{ pF}$. Calculate the oscilloscope terminal voltage ($V_i$) when the signal frequency is 100 Hz. Also determine the frequency at which $V_i$ is 3 dB below $V_s$. (c) In a percentage differential protection scheme, the current in the secondary of the current transformer at one end is 3.4 Amp and the current in the secondary of the current transformer at the other end is 3.0 Amp. The number of turns of the operating coil is 400. Determine the number of turns of the restraining coil for the balance condition. Also explain the requirement of biasing. (d) Write the modes of operation of the HVDC system. Also, write the sequence of events which take place when a large disturbance takes place near the inverter operating in the constant extinction angle control mode and the HVDC system is heavily loaded. (e) A DM system is designed to operate at 3 times the Nyquist rate for a signal with a 3 kHz bandwidth. The quantizing step size is 250 mV. (i) Determine the maximum amplitude of a 1 kHz input sinusoid for which the delta modulator does not show slope overload. (ii) Determine the post-filtered output signal-to-quantizing noise ratio for the signal of part (i).
Determine the efficiency of a 400 km long transmission line delivering 100 MW load at 240 kV, 0.85 lagging p.f. at the receiving end. The series impedance and shunt admittance per kilometre are $0.175 + j0.375$ ohm and $5 \times 10^{-6}$ mho respectively. (b) Consider a discrete memoryless source with alphabet $\{s_0, s_1, s_2\}$ and statistics $\{0.7, 0.15, 0.15\}$ for its output. (i) Apply the Huffman algorithm to this source. Hence, show that the average code-word length of the Huffman code equals 1.3 bits/symbol. (ii) Let the source be extended to order two. Apply the Huffman algorithm to the resulting extended source and show that the average code-word length of the new code equals 1.1975 bits/symbol. (iii) Compare the average code-word length calculated in part (ii) with the entropy of the original source. (c) A 3-cycle circuit breaker is connected between a generator and transformer of 20 MVA, 11 kV rating with reactances $X_d'' = 10\%$, $X_d' = 16\%$ and $X_d = 100\%$. The transformer is operating at no load and rated voltage. Determine the interrupting current and interrupting kVA by the circuit breaker when a 3-phase fault occurs between the circuit breaker and the transformer.
A 3-phase line is terminated by a star-connected resistive load of 800 ohm per phase. The line conductors are equilaterally spaced 2.0 m apart and have a diameter of 2 cm. The voltage wave travelling along the line is of 33 kV. Determine the power reflected by the load and the power consumed by the line. (b) A discrete memoryless source X has four symbols $x_1, x_2, x_3, x_4$ with probabilities $P(x_1) = 0.4$, $P(x_2) = 0.3$, $P(x_3) = 0.2$, $P(x_4) = 0.1$ respectively. I. Calculate $H(x)$. II. Find the amount of information contained in the messages $x_1, x_2, x_3$ and $x_4, x_3, x_3, x_2$ and compare with the $H(x)$ obtained in part (I). $$H = \begin{bmatrix} 1 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 0 & 1 \end{bmatrix}$$ A parity check code has the parity check matrix : $$H = \begin{bmatrix} 1 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 0 & 1 \end{bmatrix}$$ I. Determine the generator matrix G. II. Find the code word that begins with 101… III. Suppose that the received word is 110110. Decode this received word. (c) With the help of circuit diagram and phasor diagram, explain the working of a Translay relay.
A hollow cylinder made of insulating material surrounded by a thin metal sheath has inner and outer diameters of 4 cm and 8 cm respectively. The relative permittivity of the cylinder material is 4 and peak voltage gradient in air is 33 kV/cm. Determine the rms value of safe operating voltage of a conductor passing through the centre of the cylinder and having a diameter of 2 cm. (b) Show that the channel capacity of an ideal AWGN channel with infinite bandwidth is given by $$C_{\infty} = \frac{1}{\ln 2} \cdot \frac{S}{\eta} \approx 1.44 \frac{S}{\eta}$$ bit/sec. Given that : S is the average signal power and $$\frac{\eta}{2}$$ is the power spectral density of white Gaussian noise. A binary FSK system transmits binary data at the rate of $$2.5 \times 10^6$$ bits per second. During the course of transmission, white Gaussian noise of zero mean and power spectral density $$10^{-20}$$ watts per hertz is added to the signal. In the absence of noise, the amplitude of the received signal is $$1 \mu V$$ across $$50 \Omega$$ impedance. Determine the average probability of error assuming coherent detection of the binary FSK signal. (c) Write the abnormal running conditions of a generator and discuss the protection scheme against them.

Questions reproduced from the official paper for study purposes; verify on the exam-conducting body’s official website.