66 questions from the UPSC 2016 examination.
66 questions
For the circuit shown in Fig. 2(c), calculate the resistance $R_o$ as seen by the output terminals. Ignore the effect of $R_1$ and $R_2$. Assume $\beta = 99$ and $h_{ie} = 1\text{ k}\Omega$. Comment on the value of $R_o$ of the circuit :
The SCR shown in Fig. 5(c) has a $\frac{di}{dt}$ limit of $10\text{ A}/\mu\text{s}$. It is to be operated from a $100\text{ V}$ d.c. supply with load resistance $R = 50\text{ }\Omega$. (i) What is the minimum value of load inductance $L$ that will protect the SCR? (ii) If an $R_s C_s$ snubber is connected across the SCR with $R_s = 500\text{ }\Omega$, what will be the new value of load inductance $L$ to protect the SCR against $\frac{di}{dt}$?
What are the different methods of testing of circuit breakers? Discuss their merits and demerits. Which method is more suitable for testing the circuit breakers of large capacity?
The reduced incidence matrix of an oriented graph is given as \[ \begin{bmatrix} 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 1 \end{bmatrix} \] (i) Draw the graph. (ii) How many trees are possible for this graph? (iii) Write the tie-set matrix.
Write down the ALP (Assembly Language Program) to exchange 10H data bytes stored from memory location 2450H with data bytes stored from memory locations 2480H onwards.
A 3-phase, 4-pole, $50\text{ hp}$, $440\text{ V}$, $60\text{ Hz}$, $Y$-connected induction motor has the following parameters per phase : \[ \begin{aligned} r_1 &= 0\cdot10\text{ }\Omega, & x_1 &= 0\cdot35\text{ }\Omega \\ r_2' &= 0\cdot12\text{ }\Omega, & x_2' &= 0\cdot40\text{ }\Omega \end{aligned} \] It is known that the stator core loss amounts to $1200\text{ W}$ and the rotational losses equal $950\text{ W}$. Moreover, at no-load the motor draws a line current of $18\text{ A}$ at a power factor of $0\cdot089$ lagging. When the motor operates at a slip of $2\cdot5\%$, find the input line current and power factor.
A class-A chopper circuit is supplied from a d.c. source voltage $100\text{ V}$. The chopper supplies power to a series $R-L$ load with $R = 0\cdot5\text{ }\Omega$ and $L = 1\text{ mH}$. The chopper switch is ON for $1\text{ ms}$ in an overall period of $3\text{ ms}$. Calculate average load voltage, maximum and minimum value of load current and average load current. Assume continuous current operation of the chopper.
Two ideal and identical junction diodes are connected as shown in Fig. 1(d). If the current through the reverse-biased diode is $I_0$ and is constant, explain the circuit operation when both the diodes are connected in forward-biased condition. Assume $V_T = 25\text{ mV}$, $V_V = 0\cdot7\text{ V}$ and $\eta = 1$ for the diodes.
A system consists of two plants connected by a transmission line and a load at power plant 2 as shown in Figure 2(b). Data for the loss equation consists of the information that 200 MW transmitted from plant 1 to the load results in a transmission loss of 20 MW. Find the optimum generation schedule considering transmission losses to supply a load of 204.41 MW. Also evaluate the amount of financial loss that may be incurred if at the time of scheduling transmission losses are not co-ordinated. Assume that the incremental fuel cost characteristics of plant 1 and plant 2 are given by dF_1 / dP_1 = 0.025 P_1 + 14 Rs/MWh, dF_2 / dP_2 = 0.05 P_2 + 16 Rs/MWh
Compare Amplitude Modulation (AM) and Frequency Modulation (FM).
For the circuit shown in Fig. 2(a), find the value of $V$, if the power dissipation in the load resistance $R_L$ is $36\text{ watts}$ :
Eight messages are generated by a source with the following probabilities: Message m_i: m_0, m_1, m_2, m_3, m_4, m_5, m_6, m_7. Probability p_i: 0.02, 0.04, 0.07, 0.10, 0.13, 0.18, 0.22, 0.24. (i) Use Huffman scheme to code these messages. (ii) Explain and illustrate the prefix property of the code. (iii) Determine the average number of bits per message (1) with the Huffman coding, and (2) with uniform coding assuming the messages to be equiprobable. Also find the information content (entropy) in the message and hence efficiency of the Huffman coding.
Derive an expression for Maxwell's equation in integral form from Ampere's law.
An accelerometer has an input range of 0 - 100 m/s^2. It has a mass of 10 g and works on a frequency of 10 Hz. Find the range for the displacement transducer used to measure the displacement of the accelerometer.
A single-phase full-bridge square-wave inverter is supplying power to a purely resistive load of $20\text{ }\Omega$. The d.c. source voltage is $600\text{ V}$. If the inverter is to operate at $500\text{ Hz}$ with an r.m.s. load voltage $500\text{ V}$, find— (i) average power absorbed by the load; (ii) average source current (assume no losses in switching); (iii) average current of each switch.
What is a PLA? Realize the following functions using an appropriate PLA : \[ \begin{aligned} f_1 &= AB + CD \\ f_2 &= \overline{A}B + A\overline{B} \\ f_3 &= AD + \overline{B}\overline{C} + \overline{B}\overline{D} \end{aligned} \]
Write a short note on white noise.
(i) A transmission line has the following parameters : \[ Z_L = (200 - j200)\text{ }\Omega, \quad Z_0 = 200\text{ }\Omega \] Determine the voltage standing wave ratio and reflection coefficient of the line. (ii) (1) Write the significance of Smith chart. (2) Find the length of $x$ of the $100\text{ }\Omega$ transmission line which converts a load impedance $Z_L = (100 + j100)\text{ }\Omega$ to a pure resistance. Also find the value of the resistance $R_x$. Assume $\text{VSWR} = 2\cdot6$.
Show that the maximum non-linearity on account of loading of a linear potentiometer can be expressed as (400 R_p) / (27 R_m) % of f.s.d. for R_p / R_m << 1.
A circuit breaker interrupts the magnetising current of a 100 MVA transformer at 220 kV. The magnetising current of the transformer is 5% of the full load current. Determine the maximum voltage which may appear across the gap of the breaker when the magnetising current is interrupted at 53% of its peak value. The stray capacitance is 2500 muF and the inductance is 30 H.
Describe the principle of numerical protection. How is this method of protection different from conventional methods?
A 500 Hz triangular wave with a peak amplitude of 40 V is applied to the vertical deflecting plates of a CRO having a vertical deflection sensitivity of 0.1 cm/V. Another 250 Hz sawtooth wave of 50 V is applied to the horizontal plates having a horizontal deflection sensitivity of 0.08 cm/V. Assuming the two inputs are synchronized, sketch the waveform displayed on the CRO.
Explain the operations of phase-locked loop used as FM demodulator with neat sketch.
Identify the circuit shown in Fig. 6(a). Briefly explain the same. Calculate the current $i$ and $V_o$, if $V_R = 5\text{ V}$ and $R = 5\text{ k}\Omega = R_F$ :
If a propagating wave in free space has a potential gradient at any point $(x, y, z)$ as \[ \overline{E} = (\hat{i} - 2\sqrt{3}\hat{j} + 3\hat{k})e^{-j\,0\cdot04\,\pi\,(\sqrt{3}x - 2y - 3z)}\text{ V/m} \] then determine— (i) the vertical direction of propagation; (ii) the wavelength of the propagating wave; (iii) the frequency of the propagating wave; (iv) the phase velocity and phase velocity vector. What are the apparent velocities and wavelengths along $x$, $y$ and $z$ directions?
Consider a continuous-time LTI system for which the input $x(t)$ and output $y(t)$ are related by the following differential equation : \[ \frac{d^2 y(t)}{dt^2} - \frac{dy(t)}{dt} - 2y(t) = x(t) \] Determine the impulse response, $h(t)$, of the system for the following cases by plotting pole-zero pattern : (i) The system is causal. (ii) The system is stable. (iii) The system is neither stable nor causal.
The open loop transfer function of a unity negative feedback control system is given by G(s) = K / ((s + 2)(s + 4)(s^2 + 6s + 25)). For what value of K, will the system work as an oscillator in its closed loop form?
What is Load Flow solution? What do you understand by (i) Adjustable Load Flow, and (ii) Unadjustable Load Flow? Which method will provide the accurate solution?
Compare memory mapped I/O (Input/Output) with peripheral mapped I/O for 8085 microprocessor.
Write down the purpose of each bit in SIM (Set Interrupt Mark) instruction. Give three different functions of SIM instruction.
1. State and explain Nyquist criterion. 2. An information signal x(t) = 5 cos(2000) pi t cos(5000) pi t is sampled. Calculate the minimum sampling rate that will be needed to recover the signal back from its samples.
(i) Calculate the value of reactance that should be placed in the generator neutral such that the current for single line-to-ground fault does not exceed the rated current. (ii) What value of the resistance in the neutral will serve the same purpose?
What do you mean by aliasing? How can aliasing be removed? State and explain Shannon's sampling theorem.
Form [B'] and [B''] matrices used in Fast Decoupled Load Flow (FDLF) for the power system shown in Figure 5(b) and line data given in Table I.
(i) Figure 2(a) shows the block diagram of a control system. Find its characteristic equation. (ii) Calculate its damping factor and undamped natural frequency for K = 10. (iii) What should be the value of K for critical damping? (iv) For K = 10, find the expression for c(t) and obtain the time at which the first overshoot occurs. Also calculate the peak overshoot magnitude.
For the circuit shown in Fig. 3(c), get the expression for $V_o$. Also sketch the output waveform. Assume that the op-amp is ideal. $R = \sqrt{\frac{L}{C}}$, $\omega = \frac{1}{\sqrt{LC}}$ and $V_i = 10\sin\omega t$ :
An 820 omega resistance with an accuracy of plus or minus 10% carries a current of 10 mA. The current was measured by an analog meter of 25 mA range with an accuracy of plus or minus 2% of full scale. Compute the power dissipated in the resistor and determine the accuracy of the result.
With the help of a neat diagram, explain the functioning of a Ramp type Analog-to-Digital Converter. A Ramp type ADC makes use of a 1 MHz clock generator and a ramp voltage that increases from 0 - 1.25 V in 125 ms. Find the number of clock pulses counted into the register for an input of 0.75 V.
The open loop transfer function of a system is given by G(s) = 5 / (s(s + 2)). It is desired to locate the poles of this transfer function at -8 and -3 plus or minus 4j by using a suitable PID controller. Find the suitable gains needed by the PID controller to achieve this task.
A $200\text{ V}$, $875\text{ r.p.m.}$, $150\text{ A}$, separately excited d.c. motor has an armature resistance of $0\cdot06\text{ }\Omega$. The motor armature terminals are fed from a single-phase fully controlled bridge rectifier. The input a.c. supply to bridge rectifier is $240\text{ V}$, $50\text{ Hz}$. Assuming continuous and ripple-free armature current, determine the following : (i) Firing angle of SCRs for rated torque and $750\text{ r.p.m.}$ (ii) Firing angle for rated torque and $-500\text{ r.p.m.}$ Assume that field winding of the motor is connected to a constant d.c. voltage source.
Consider a control system with characteristic equation s(s + 4)(s^2 + 2s + 2) + K(s + 1) = 0. Draw complete root loci labelling all important values. Find the angles of asymptotes and the intercept of asymptotes.
With the help of a neat diagram, explain the working of an LVDT. Give its characteristics, advantages and applications. Explain the role of phase sensitive detector used for signal conditioning of LVDT.
Consider the system described by [dot{x}_1; dot{x}_2] = [-4 -1; 3 -1][x_1; x_2] + [1; 1]u, y = [1 0][x_1; x_2]. Obtain the transfer function of the system.
Explain with proper transfer function a standard PID controller. Explain why derivative term is not employed alone.
Discuss and differentiate between ISO/OSI and TCP/IP. Explain how the functions of each of the seven layers of ISO/OSI are carried out by TCP/IP.
Assume that the accumulator contains data byte 82H and the instruction MOV C, A (4FH) is fetched. List the steps in decoding and executing the instruction.
(i) Determine the propagation constant $\gamma$ for a material having $\mu_r = 1$, $\varepsilon_r = 8$ and $\sigma = 0\cdot25\text{ pS/m}$, if the wave frequency is $1\cdot6\text{ MHz}$. (ii) Find the skin depth $\delta$ at a frequency of $1\cdot6\text{ MHz}$ in aluminium, where $\sigma = 38\cdot2\text{ MS/m}$ and $\mu_r = 1$. Also find $\gamma$ and the wave velocity $u$.
Discuss the concept of 'Hamming distance'. How is the minimum Hamming distance between a set of code words related to the error detection and error correction properties of the code? Find the correct 4-bit messages from the following two Hamming codes, assuming at most a single error has occurred: C_1 = 011010, C_2 = 1011001
Determine the overall impulse response, $h(n)$, of the system shown in Fig. 1(b) below. Given that $h_1(n) = \delta(n) - \left(\frac{1}{5}\right)\delta(n-1)$ $h_2(n) = \delta(n) - \delta(n-1)$ $h_3(n) = \left(\frac{1}{5}\right)^n u(n)$ $h_4(n) = (n-1)u(n)$ $h_5(n) = \delta(n) + nu(n-1) + \delta(n-2)$ where $\delta(n)$ and $u(n)$ denote, respectively, the unit impulse and unit step signals :
Show that the (7, 4) cyclic codes generated by the two polynomials g_1(P) = P^3 + P^2 + 1, and g_2(P) = P^3 + P + 1 are equivalent. Find the codes for the four messages: (0011), (0101), (1010), (1101)
An LVDT is connected to a 10 V voltmeter through an amplifier of gain 100. An output of 2 mV appears across the terminals of the LVDT when the core crosses a distance of 0.5 mm. Find the sensitivity of the LVDT and that of the whole set-up. The used voltmeter has 100 divisions and 1/5th of a division can be read accurately. Find the resolution of the instrument in mm.
Minimize the SOP terms given for a Boolean function \[ f(A, B, C, D) = \sum m(2, 3, 8, 10, 11, 12, 14, 15) \] Implement the minimized function using NAND gates alone.
What do you mean by V-curves of a synchronous motor? Draw them showing the leading power factor and lagging power factor regions.
Discuss the operating principle of SF_6 circuit breaker. What are its advantages over other types of circuit breakers? In practice, for what voltage range is it recommended?
Determine the causal signal, $x(n)$, having its $z$-transform \[ X(z) = \frac{1}{(1 + z^{-1})(1 - z^{-1})^2} \]
Two impedances $Z_1 = 5\text{ }\Omega$ and $Z_2 = (5 - jX_C)\text{ }\Omega$ are connected in parallel and this combination is connected in series with $Z_3 = (6\cdot25 + j1\cdot25)\text{ }\Omega$. Determine the value of capacitance of $X_C$ to achieve resonance if the supply is $100\text{ V}$, $50\text{ Hz}$.
Obtain the dotted equivalent circuit for the coupled circuit shown in Fig. 3(a) and hence find the voltage across the capacitor :
Describe the function of each of the following mnemonics. How many cycles do each of them require for execution and which are the flags affected? Explain. 1. DAD (Double Add) 2. CMC (Complement Carry) 3. LHLD (Load H-L Register Pair Direct) 4. ORI (OR Immediate)
For the op-amp circuit shown in Fig. 4(c), deduce the output voltage expression. Calculate $V_o$, when $R_1 = 1\text{ k}\Omega = R_2$, $R_3 = 1\text{ K}$ and $R_4 = 2\text{ K}$ and $V_{\text{in}} = 1\text{ V}$ :
Identify the relevant layers of the ISO/OSI model to which the following protocols belong: SQL, HTTPS, ISDN, PPP, NFS, IP, RPC, TELNET, HDLC, X Windows
Explain Delta Modulation, comparing it with Differential Pulse Code Modulation. Discuss how the choice of step size in Delta modulator affects slope overload distortion and granular noise.
The resistances and leakage reactances of a $10\text{ kVA}$, $50\text{ Hz}$, $2300/230\text{ V}$ distribution transformer are \[ r_1 = 3\cdot96\text{ }\Omega \text{ and } r_2 = 0\cdot0396\text{ }\Omega, \; x_1 = 15\cdot8\text{ }\Omega \text{ and } x_2 = 0\cdot158\text{ }\Omega \] Subscript $1$ refers to $\text{HV}$ and $2$ refers to $\text{LV}$ winding The transformer delivers rated $\text{kVA}$ at $0\cdot8\text{ p.f.}$ lagging to a load on the $\text{LV}$ side. Find the $\text{HV}$ side voltage necessary to maintain $230\text{ V}$ across load terminals. Also find the percentage voltage regulation.
A $20\text{ hp}$, $230\text{ V}$, $1150\text{ r.p.m.}$ d.c. shunt motor has four poles, four parallel armature paths and $882$ armature conductors. The armature circuit resistance is $0\cdot188\text{ }\Omega$. At rated speed and rated output, the armature current is $73\text{ A}$ and the field current is $1\cdot6\text{ A}$. Calculate the electromagnetic torque.
Explain the following terms in reference to performance indices in a control system: 1. Rise time 2. Integral square error 3. Integral of time multiplied square error 4. Integral absolute error 5. Integral of time multiplied absolute error
Two sub-stations are connected by two lines in parallel with negligible impedance, but each containing a tap-changing transformer of reactance 0.18 p.u. on the basis of its rating of 200 MVA. Find the net absorption of reactive power when the transformer taps are set to 1:11 and 1:0.9 respectively. Assume p.u. voltages to be equal at the two ends and also at the sub-stations.
Explain in detail about pre-emphasis and de-emphasis in Frequency Modulation (FM).