**Ques.1. ** The time constant of the casual system represented by G(s) = 1/(s+5) is:-

- 5 sec
- 0.2 sec
- π/10
- π/5

**Answer.2. 0.5 sec**

**Explanation:-**

The given equation above i.e G(s) = 1/(s + 5) is in Pole-zero form. Now converting it into standard Transfer function form i.e G(s) = K/(τs + 1) we get

= 1/5 (s/5 + 1)

Time constant τ = 1/5 sec = 0.2 sec

**Ques.2.** A BJT biasing circuit is shown in the figure. The transistor is operating in the active region with V_{BE} = 0.7 V. The value of collector current in mA is

IMG

- 210
- 813
- 817
- 512

**Ques.3.** A Buchholz relay is used for

- A Protection of a transformer against external faults
- Protection of a transformer against internal faults
- Protection of a transformer against internal and external faults
- None of the options

**Answer.2. Protection of a transformer against internal faults**

**Explanation:-**

‘Buchholz” Relay on power transformers using a conservator liquid-preservation system, a “Buchholz” relay can be installed in the piping between the main transformer tank and the conservator.

The purpose of the Buchholz relay is to detect faults that may occur in the transformer. One mode of operation is based on the generation of gases in the transformer during certain minor internal faults.

Gases accumulate in the relay, displacing the liquid in the relay until a specified volume is collected, at which time a float actuates a contact or switch.

Another mode of operation involves sudden increases in pressure in the main transformer tank, a sign of a major fault in the transformer. Thus due to fast reduce the level of oil, the pressure in the tank increases. This energizes the trip circuit which opens the circuit breaker. Thus the transformer is totally disconnected from the supply.

For the economic considerations, Buchholz relays are not provided for the transformers having a rating below 500 kVA.

**Ques.4.** Two Inductors of 5 H and 4 H have a mutual inductance of 2.5 H between them. The coupling coefficient is

- 47
- 78
- 125
- 0.56

**Answer.4. 0.56**

**Explanation:-**

Coupling Coefficient K = M/√L_{1}.L_{2}

Mutual Inductance M = 2.5 H

Inductance L_{1} = 5 H

Inductance L_{2} =4H

K = 2.5/√5×4

K = 0.56

**Ques.5.** A load-flow program is run twice. In the second run, the previous reference bus gets changed to a PQ bus. Which one of the following statements is true?

- The system losses, as well as complex bus voltages, will change.
- The load flow result will remain the same in all aspects.
- The system losses will be unchanged but the complex bus voltages will change.
- The system losses will change but the complex bus voltages will remain the same.

**Ques.6.** The impulse response of a casual linear time-invariant system is given as h(t). Now consider the following two statements:

P: The system satisfies the superposition principle.

Q: h(t) = 0 for t < 0.

Which of the following is true?

- P is false and Q is false.
- P is true, and Q is false.
- P is true and Q is true.
- P is false and Q is true.

The impulse response function (IRF) of a dynamic system is defined as the output of the IRF when an impulsive input signal is added to the system. Since the impulse function contains all frequencies, the impulse response defines the response of a linear, time-invariant system for all frequencies.

The impulse response of a linear system h_{T}(τ) is the output of the system at time t to an impulse at time τ. This can be written as

**h _{T }= H(δ_{τ})** hτ (t) = H(δτ (t))

**Linearity Property**

The system is said to be linear if it obeys two important properties.

**Homogeneity****(Scaling)****Superposition****(Additivity)**

Most digital signal processing (DSP) techniques also require the system to be shift-invariant even though it is not a requirement for linearity. Note that a system is said to be time-invariant or shift-invariant if its input-output characteristics do not change with time.

**Homogeneity Property:-** The system is said to obey the property of homogeneity if the following condition holds:

For input signal of x(n) if the output is given by y(n) then for an input signal of kx(n) the output is ky(n), where k is any scaling factor.

y(n) = kx(n)

**Superposition** **(Additivity):-**

Let y_{1}(n) be the output for the input signal x_{1}(n) and y_{2}(n) be the output for input signal x_{2}(n) for a system. The property of additivity states that

If the input to a system is the addition of two signals x_{1}(n) and x_{2}(n) then the output of the system is the addition of the respective outputs, namely, y_{1}(n) and y_{2}(n).

K_{1}x_{1}(n) + K_{2}x_{2}(n) = K_{1} y_{1}(n) + K_{2} y_{2}(n)

Linear Systems: A system is said to be linear if a system operator satisfies the conditions of both homogeneity (scaling) and additivity (superposition). Otherwise, a system is nonlinear.

**Characteristics of continuous time LTI system:-**

**Causality:- **For causal continuous time LTI system, we have h(t) = 0, t < 0

Let T be an LTI system that is in the ground state. Let us apply a unit impulse function, δ(t) as input to T at t = 0. So, for t < 0, x(t) = 0 and since the system has been assumed to be in-ground state, its output y(t) which in the present case, is h(t), must be zero for all t < 0.

Since the system, being causal cannot anticipate the input that is going to be applied to it at t = 0 and produce an output. At t = 0, the impulse is applied as input and so for t = 0, the output, h(t), need not be zero.

Thus, for any causal LTI system, h(t) = 0 for t < 0.

**Ques.7.**

**Ques.8. **An Ideal air-core coil has an inductance of 2 mH. The number of turns of the coil is doubled and its length is halved. Assuming that the inner cross-sectional area of the core remains constant, the new inductance of this altered air-core coil is

- 4 mH
- 16 mH
- 8 mH
- 32 mH

**Ques.9.** Find the equivalent resistance Req looking at the terminal of the following circuit as indicated

IMG

- 10Ω
- 2 Ω
- 4 Ω
- 4 Ω

**Ques.10.** In a balanced acb sequence, phase to neutral voltage is V_{an} = 100 ∠20° V. line-to-line voltage Vac is given by

- V
_{ac}= 100∠50° V - V
_{ac}= 100√3∠-50° V - V
_{ac}= 100/√3∠150° V - V
_{ac}= 100√3∠50° V

**Ques.11.** The inductance of a power transmission line increases with

- Increase in diameter of the conductor
- Increase in spacing between the phase conductors
- The decrease in line length
- Increase in load current carried by the conductor

**Ques.12.** The effective charge flowing through a wire is given by, q = 5t sin4πt mC. Calculate the instantaneous current flowing at time t = 0.5 s.

- 4 mA
- 0 A
- 14 A
- 5 mA

**Ques.13.** In the given circuit, with the shown ideal 5V DC source, the magnitude of the total current drawn from the source at steady-state is

IMG.

- 10 A
- 5 A
- 5 A
- 5 A

**Ques.14.** A three-winding transformer is connected to an AC source with 50 V RMS as shown in the following figure. Voltages induced in the secondary windings are 2 V RMS and 8 V RMS. The output RMS voltage V_{o} is,

img

- 6 V
- 10
- -6V
- -10V

**Ques.15. **The open-loop gain-bandwidth product of an op-amp is given as 10,000 Hz. The op-amp is used in an inverting amplifier as shown in the figure. The bandwidth of the Inverting amplifier is

- 5000 Hz
- 2000 Hz
- 10,000 Hz
- 1000 Hz

**Ques.16.** In the diode circuit shown in the figure, v, = 10sin314.159t V and V_{R} = 5 V. Assume the diode to be ideal. The maximum and minimum values of the output voltage (v_{o}) are, respectively,

- +5V and -10V
- -10V and +5V
- 10 V and -10 V
- + 5V and -5 V

**Ques.17.** Find the equivalent capacitance, C_{eq}, at the terminals a-b of the circuit.

- 80 μF
- 85 μF
- 20 μF
- 46 μF

**Ques.18.** To ensure successful turn-on of a thyristor, the minimum gate pulse width of the thyristor gate pulse should be sufficient to ensure the cathode current to reach

- The latching value of thyristor current
- 50% of the peak value of thyristor current
- The holding value of thyristor current
- The peak value of thyristor current

**Ques.19.** A 3-phase transformer bank is realized using three Identical 1100/230 V, 10 WA single-phase transformers connected in delta-delta. If one of the single-phase transformers develops a fault and is removed, the maximum load that the transformer bank in the open delta can supply is

- 30 kVA
- 77 kVA
- 32 kVA
- 54 kVA

**Ques.20.** The minimum phase attained for the frequency response of a causal system G (s) = s+10/ (s +1)(s +2) as the frequency varies from 0 to ∞ rad/s is

- -180
**°** - 180
**°** - -90
**°** - 90
**°**

**Ques.21.** Auto-transformer is used in the transmission and distribution systems

- When the operator is not available
- When the efficiency of the transformer is not critical
- When galvanic isolation is needed
- When the transformation ratio for voltage is small

**Ques.22.** The equation of ef = -dφ/dt where e_{f} is the emf and φ is the flux linkage in a single-turn coil, can best represent

- Faraday’s Law
- Faraday’s Law and Lenz Law
- Biot-Savart Law
- Lenz Law and Biot-Savart Law

**Ques.23. **The following are various energy sources:

- Solar
- Wind
- Tidal
- Wave
- Geo-thermal

From the above energy sources, renewable energy sources are

- 1 and 2 only
- 1, 2, and 4 only
- All the energy sources mentioned above
- 1, 2, and 3 only

**Ques.24.** Kelvin double bridge is best suited for the measurement of

- Low resistance
- Inductance
- High resistance
- Capacitance

**Ques.25.** For an ideal single-phase transformer with a primary-to-secondary turns ratio of N:1, the ratio of instantaneous input power to instantaneous output power is.

- N:1
- 1:N
- 1:1
- N
^{2}:1

**Ques.26.** The inductance of a certain moving-iron ammeter is expressed as L= 10+ 3Ɵ – Ɵ^{2}/4, where Ɵ is the deflection in radians from the zero position. The control spring torque is 25 x 10^{-6} Nm/radian. The deflection of the pointer in radians, when the meter carries current of 5 A RMS, is

- 4
- 2
- 0
- 0

**Ques.27.** The op-amp in the circuit shown in the figure works in linear mode. The output voltage V_{o} is

- 1 V
- 6 V
- 5 V
- 4 V

**Ques.28.** The purpose of emitter bypass capacitor in a CE BJT amplifier is to

- Place the Q-point of the transistor in an active region
- Increase the mid-band voltage gain of the amplifier
- Provide a stable biasing for the amplifier
- Prevent saturation of the amplifier

**Ques.29.** Consider a signal g(t), such that g(t) = 0 for t < 0. If the Laplace transform of g(t) is G (s), then with constant τ, the Laplace transform of g(t — τ) is

- G(S + τ)
- e
^{sτ}G(sτ) - G(S – τ)
- e
^{-sτ}G(sτ)

**Ques.30.** The transfer function G(S) = 1/s^{2} has a 0 dB crossing in its Bode magnitude plot at

- 10 rad/s.
- 1 rad/s.
- 100 rad/s.
- 1 rad/s.

**Ques.31. **For operation in the normal active mode for a BIT, which of the following conditions is true?

- B-E Junction should be reversed biased and C-B junction should be forward biased.
- B-E Junction should be forward biased and C-B junction should be reversed biased.
- Both B-E and C-B junctions should be forward biased.
- Both B-E and C-B junctions should be reversed biased.

**Ques.32.** The average output voltage of a half controlled bridge converter is measured to be 103.53 V. If the bridge is supplied from a 230 V, 50 Hz sinusoidal source, the triggering angle of the show in the bridge is approximate.

- 30°
- 120°
- 60°
- 90°

**Ques.33.** A transmission line of surge impedance 300 Ω is connected to a load of 300 Ω. The reflection coefficient of the transmission line at the load end will be

- 0
- −1
- +1
- 2

**Ques.34.** The compensating winding in a DC machine

- It is located on the commutating poles.
- It is located on pole shoes.
- It is located in armature slots.
- It is located on commutators.

**Ques.35.** Consider the following Laplace transforms of certain signals. For which of the following, the final value theorem is not applicable?

- (s + 1)/(s − 2)
- (s + 1)/(s + 2)
- (s + 1)/(s + 2) (s + 3)
- (s − 1)/(s + 2)

**Ques.36.** What is the total electric flux through the surface of a sphere that has a radius of 1 m and carries a charge of 1 μC at its center? Coulomb constant is given by K_{e} = 1/4πε_{o} = 8.99 x 10^{9} N. m^{2} /C^{2}; ε_{o} is the permittivity of free space.

- 8.99 x 10
^{3}N.m^{2}/C^{2} - 3.98 x 10
^{3}N/C - 1.13 x 10
^{5}N.m^{2}/C^{2} - 0.28 x 10
^{5}N.m^{2}

**Ques.37.**For a non-ideal single-phase transformer, which of the following is not true?

- An open circuit test is usually done on the low voltage side of a transformer.
- The short circuit test reveals approximately the resistance and leakage reactance of the transformer windings.
- Open circuit test can reveal resistance and leakage reactance of transformer windings.
- The open-circuit test reveals approximately the magnetizing inductance and the core-loss resistance.

**Ques.38.** The graph of an electrical network has N nodes and B branches. The number of links, L, for any tree spanning all nodes is given by

- B + N
- N − B + 1
- B − N + 1
- N − 2B + 1

**Ques.39.** A linear time-invariant system, initially at rest, when subjected to a unit step input at t = 0, gives a response y(t) = te^{−t} for t ≥ 0. The transfer function of the system is.

- 1/s(s + 1)
^{2} - 1/s
^{2} - s/(s + 1)
^{2} - 1/(s + 1)
^{2}

**Ques.40.** A DC-DC buck-boost converter is operated with the continuous current mode. If the input voltage is 50 V and the duty cycle of the switch is 0.6, the output DC voltage is

- 75 V
- 50 V
- 35 V
- 65 V

**Ques.41.** A single-phase full-bridge voltage source inverter is operated with SPWM (sinusoidal pulse width modulation). The input DC voltage is 100 V. If the amplitude modulation index is 1, the RMS value of the fundamental component of the output voltage is

- 90.7 V
- 70.7 V
- 141.4 V
- 50.3 V

**Ques.42.** An electrostatic field is given by K. = (x/2 + 2y) i + 2x j V/m. Find the work done in moving a point charge Q = —20 μC from the origin to (4,0,0) m. (i, j) are the unit vectors along x, y-axis.

- 40 kJ
- 80 μJ
- 40 μJ
- 80 J

**Ques.43.** In the given Wheatstone bridge, R_{1} = 500 Ω, R_{3} = 200 Ω. The bridge is balanced when R_{2} is adjusted to 125 Ω. Determine the unknown resistance R_{x}.

- R
_{x}= 125 Ω - R
_{x}= 100 Ω - R
_{x}= 200 Ω - R
_{x}= 50 Ω

**Ques.44.** A single-phase power transformer is to be energized (switched on to the input supply) to have minimal inrush current. The switching-on instant should be at

- 1/√2 of the maximum input voltage
- Maximum input voltage
- 1/2 of the maximum input voltage
- Zero input voltage

**Ques.45.** A parallel-plate capacitor has an area A = 2 x 10^{−4} m^{2} and a plate separation d = 1 mm. The permittivity of free space, ε_{o} = 8.85 x 10-^{12} — Its capacitance is, C^{2}/N.m^{2}

- 1.77 pF
- 4.23 nF
- 4.23 μF
- 1.77 nF

**Ques.46.** The causal system represented by G (s) = 9/s^{2}+6s+9 is

- Critically damped
- Undamped
- Underdamped
- Overdamped

**Ques.47.** The SCR in the circuit is turned on at t = 0. The conduction time duration of the SCR is

IMG

- 2π√LC
- √LC
- 1/(2π√LC)
- π√LC

**Ques.48.** A triac based single-phase voltage regulator feeds an R-L load as shown in the figure. What is the range of triggering angle for which the output voltage vo is not controllable?

- 0°≤ α ≤ 45°
- 90°≤ α ≤ 180°
- 45°≤ α ≤ 90°
- 45°≤ α ≤ 180°

**Ques.49.** A water boiler at a home in Lucknow is switched to the AC mains supply power. The frequency of instantaneous power consumed by the boiler is

- 50 Hz
- 100 Hz
- 150 Hz
- 0 Hz

**Ques.50.** A circuit with a resistor, inductor, and capacitor in series has a resonant frequency of f_{o} Hz. If all the component values are now doubled, the new resonant frequency is

- f
_{o}/4 - 2f
_{o} - f
_{o} - f
_{o}/2

**Ques.51.** A charge q_{1}= 7µC is located at the origin, and a second charge q_{2} = —5µC is located on the positive x-axis, 0.3 m from the origin. Find the electric field at point P, which has coordinates (0, 1 0.4) m. Coulomb constant is given by, K_{e} = 1/4πε_{o} = 8.99 x 10^{9} N. m^{2} /C^{2}; ε_{o} is the permittivity of free space. (i, j) are the unit vectors along x, y-axis.

- −(1.1 î + 2.5 ĵ ) × 10
^{5}N/C - −(2.5 î + 1.1 ĵ ) × 10
^{5}N/C - (2.5 î − 1.1 ĵ ) × 10
^{5}N/C - (1.1 î + 2.5 ĵ ) × 10
^{5}N/C

**Ques.52.** The Zener diode in the circuit has a Zener voltage, V_{Z} of 15 V and power rating of 0.5 Watt. If the input voltage is 40 V, what is the minimum value of R_{S} that prevents the Zener diode from being destroyed?

- 150 Ω
- 250 Ω
- 750 Ω
- 500 Ω

**Ques.53.** In a boost converter shown in the figure, the duty cycle is 0.5. The inductor current is assumed to be continuous. Capacitor C is assumed to be very large. If the switching frequency is 20 kHz, the peak to peak inductor current ripple is

- 02.5 A
- 0.45 A
- 0.15 A
- 0.05 A

**Ques.54.** In the circuit shown, assume that the voltage source and transformers are ideal. The AC voltage source is 10√2sin(100πt) V. The RMS value of the current flowing through the 1Ω resistors is approximately (rounded off till first decimal place)

- 0.1 A
- 0.9 A
- 9.1 A
- 10.0 A

**Ques.55.** A single-phase full-bridge voltage source inverter is operated in 180° mode with square wave output. If the input DC supply is 100 V, the RMS value of the fundamental output voltage is

- 80 V
- 50 V
- 70 V
- 90 V

**Ques.56.** The switch in the circuit has been closed for a long time, and it is opened at time t = 0. Find v(t) for t ≥ 0.

- v(t) = 15 e
^{−20t}V - v(t) = 15 e
^{−5t}V - v(t) = 0 V
- v(t) = 15 V

**Ques.57.** A sinusoidal AC voltage source feeds a pure inductor through a diode as shown in the figure. The duration of conduction (in degrees) of the diode in one input power cycle is

- 30°
- 90°
- 360°
- 180°

**Ques.58.** An ammeter with a range of 0 to 100 μA has an internal resistance of 100 Ω. For extending its range to 0 to 500 μA, the shunt resistance required is

- 22.22 Ω
- 25 Ω
- 50 Ω
- 20 Ω

**Ques.59.** A power system has three synchronous generators. The turbine-governor characteristics corresponding to the generators are

P1 = 50(50 — f), P2 = 100(51 — f), P3 = 150(52 —1)

where, f denotes the system frequency in Hz, and P1, P2, P3 are the power outputs of the turbines in MW. Assuming generators and transmission network to be lossless, the system frequency for a load of 700 MW is

- 49 Hz
- 48.5 Hz
- 47 Hz
- 49.5 Hz

**Ques.60.** The positive value of K for which [l + K/ (s+1)(s+2)] will have zeroes on the right-half of the

complex s-plane is

- 10
- 0.1
- No such K exist
- 20

**Ques.61.** Consider the system in the figure shown. The input to the system is R(s) and the output of the system is C(s). The system is of Type

- 0
- 3
- 2
- 1

**Ques.62.** A factory draws 100 kW at 0.8 p.f. lagging from a 3-phase, 11 kV supply. It is desired to raise the p.f. to unity using the capacitor bank. The total power rating of the capacitor bank is

- 75 KVAR
- 100 KVAR
- 50 KVAR
- 62.5 KVAR

**Ques.63.** A BJT current source is given in the figure. Assume the Si-PNP transistor operates in an active region. The value of current I in mA is

- 2.15 A
- 1.85 A
- 4.1 A
- 5.25 A

**Ques.64.** A single-phase AC distribution line supplies two single-phase loads as shown in the figure below. The impedances of line segments A-B and B-C are j125 Ω and j0.35 Ω, respectively. The voltage drop from A to C is

IMG

- 30 − j4.5 V
- 4.5 − j30 V
- 4.5 + j30 V
- 30 + j4.5 V

**Ques.65.** An open circuit test is conducted on a 1100/110 V, 50 Hz single-phase transformer with instruments connected on the low voltage side of the transformer. The voltmeter reads 110 V. The ammeter reads 2 A. The wattmeter reading is 65 W. The approximate core-loss resistance and magnetizing reactance, referred to the low voltage side, are respectively.

- 186.15 Ω, 57.57 Ω
- 18.615 Ω, 5.757 Ω
- 1.8615 Ω, 0.5757 Ω
- 18615 Ω, 5757Ω

**Ques.66.** A current of −8 + 6√2(sinωt +30°)A is passed through three meters. These are a zero-centered PMMC meter, a true RMS meter, and a moving iron instrument. The respective readings (in A) will be

- 8, 6, 10
- −8, 10, 10
- -8, 6, 10
- 8, 6, 8

**Ques.67.** For the circuit shown in the figure, find the node voltages v_{1} and V_{2}.

- V
_{1}= 6 V and V_{2}= 8 V - V
_{1}= 4 V and V_{2}= −28 V - V
_{1}= 8.33 V and V_{2}= 10.33 - V
_{1}= −7.33 V and V_{2}= −5.33 V

**Ques.68.** Find Norton equivalent resistance, R_{N}, and equivalent current source, I_{N}, at terminals a and b of the circuit.

- R
_{N}= 5 Ω, I_{N}= 2 A - R
_{N}= 3.53 Ω, I_{N}= 0.71 A - R
_{N}= 4 Ω, I_{N}= 1 A - R
_{N}= 12 Ω, I_{N}= 2 A

**Ques.69.** The terminal voltage of an ideal DC voltage source is 12 V when connected to a 2 W resistive load. When the load is disconnected, the terminal voltage rises to 12.4 V. What are the values of source voltage, V_{S}, and internal resistance, R_{s}, of the source?

- V
_{S}= 12.4 V, R_{S}= 4Ω - V
_{S}= 10 V, R_{S}= 8Ω - V
_{S}= 12.4 V, R_{S}= 2.4Ω - V
_{S}= 12 V, R_{S}= 4Ω

**Ques.70. **A 240 V DC shunt motor has an armature resistance of 0.6 Ω. The full load armature current is 30 A. The ratio of the stalling torque to the full load torque when the resistance of 1 Ω is connected in series with the armature is

- 3
- 5
- 6
- 4

**Ques.71.** Incremental fuel costs in Rs/MWh for a plant consisting of two generating units are given by

dF_{1}/dp_{1} = 0.4P1 +400 and dF_{2}/dp_{2} = 0.48P_{2} + 320.

The allocation of loads P_{1} and P_{2} between generating units 1 and 2, respectively, for the minimum cost of generation to serve a total load of 900 MW, neglecting losses, is

- 500 MW and 400 MW
- 400 MW and 500 MW
- 200 MW and 700 MW
- 300 MW and 600 MW

**Ques.72.** A segment of a circuit is shown in the figure below. If VR = 5 V and Vc= 4sin2t V, the voltage V_{L} is

- 32 sin2t V
- 16 cos2t V
- 3 − 8cos2t V
- 16 sin2t V

**Ques.73. **A combinatorial circuit is described by a function as the sum of min-terms. The function is defined as f(A,B,C) = Σm(0,1,2,3,4,5,6) . A is the MSB and C is the LSB. The minimized expression of the function is

- B̄ + C̄
- Ā + B̄ + C̄
- ABC
- Ā + B̄ + C

**Ques.74.** A sequence u[n] is defined as

Consider a sequence x[n] = n^{2}a^{n}u[n], where a is a positive constant. The z-transform of the sequence with an appropriate region of convergence is

- az(z + a)/(z − a)
^{3} - z/(z − a)
^{2} - az/(z − a)
^{3} - ze
^{−α}/(z − e^{−α})2