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80 questions. The official answer key for this paper has not been published on CMB HUB yet, so the questions are shown without answers.
A 50 MHz uniform plane wave is propagating in a material with relative permeability and relative permittivity as 2.25 and 1 respectively. The material is assumed to be loss less. Find the phase constant of the wave propagation.
A non-magnetic lossy dielectric material with relative permittivity εr = 2.25 and conductivity σ = 10^-4 mho/m is applied with electromagnetic wave of 2.5 MHz. What is the loss tangent?
A solid conductor with relative permeability µr = 200, conductivity σ = 5 × 10^6 mho/m having outer dia 8 mm and length 2 mm. If the total current carried by the conductor is i(t) = 2 cos(π10^4 t) A. Find the skin depth.
A uniform plane wave at the boundary of an overhead transmission line and underground cable has reflection coefficient: γ. The standing wave ratio is
Working principle of thermo-couple is
Which of the following represents a stable system?
Of following transfer function of second order linear time-invariant systems, the under damped system is represented by?
Which of the following measures cannot be effective in reducing the noise?
Assuming leakage flux to be negligible, when HV side of a single-phase 100 V/50 V, 50 Hz transformer is connected to 50 V, 25 Hz AC source, the core flux of the transformer is
The Schmitt trigger circuit shown in the figure below uses Zener diode with Vd = 0.7 V. If the threshold voltage V1 is zero and hysteresis voltage VH = 0.2 V, then what is R1/R2 and VR? [Figure description: An op-amp Schmitt trigger. Vin is applied to the inverting (-) input. The non-inverting (+) input node (voltage V1) is connected through resistor R1 to the op-amp output V0, and through resistor R2 to a reference voltage VR. The output V0 is clamped to ground by two back-to-back Zener diodes (each labelled Vz).]
For a given relation √(1 - x^2) + √(1 - y^2) = P(x - y), where P is a constant, the value of dy/dx at point (0, 0) is
The integral from 0 to 1 and 0 to x^2 of (x^2 + y^2) dx dy equals to
An open-loop system represented by the transfer function, G(s) = (s - 1)/((s + 2)(s + 3)) is
A load center of 120 MW derives power from two power stations connected by 220 kV transmission lines of 25 km and 75 km as shown in figure below. The three generators G1, G2 and G3 are of 100 MW capacity each and have identical fuel cost characteristics. The minimum loss generation schedule for supplying the 120 MW load is [Figure description: Generator G1 on the left is connected through a 25 km line to a bus where the 120 MW load is tapped; from this bus a 75 km line goes to a bus feeding two generators G2 and G3 in parallel on the right.]
A capacitor is made with a polymeric dielectric having a relative permittivity εr of 2.26 and a dielectric breakdown strength of 50 kV/cm. The permittivity of free space is 8.85 pF/m. If the rectangular plates of 20 cm and a length of 40 cm, then the maximum electric charge in the capacitor is
For a circuit shown below calculate the value of i1? [Figure description: A 10 V source on the left feeds a vertical divider of two 10 kΩ resistors (top and bottom) whose midpoint carries current i1 to the right through a 0.7 V source (+ on left, - on right). The right node connects to a dependent current source 10 i1 (arrow pointing down into the node from a 20 V supply on the top right), and a 1 kΩ resistor to ground. A 20 V source is at the far right connected between the top wire and ground.]
Calculate v1 for the circuit given below? [Figure description: A circuit with a 3 Ω resistor across the top (v1 measured + left to - right across it); below it, a 2 Ω resistor and a 5 Ω resistor in series along a middle wire with a common node between them. A 2 A current source (arrow up) on the left, a dependent voltage source 4V1 (+ on top) connected from the middle node to the bottom rail, and a dependent current source V1 (arrow up) on the right.]
What is Laplace transform of function e^(-5t) cos 4t?
Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4. How many distinct 4 digit numbers greater than 3000 can be formed using these digits?
The characteristic equation of a 3 × 3 matrix P is defined as : |λI - P| = λ^3 + λ^2 + 2λ + 1 = 0. "I" denotes identity matrix, then inverse of matrix P will be :
A function y(t) satisfies the following differential equation: dy(t)/dt + y(t) = δ(t). Where δ(t) is unit impulse function and u(t) is unit step function. Assuming zero initial conditions, what is y(t)?
A solid non-magnetic conductor of circular cross section has its axis on z-axis and carries a uniformly distributed total current of 60 A in the az direction. If the radius of the conductor is 4 mm, find the magnetic flux density at ρ = 5 mm.
The magnetic flux density in a magnetic material with susceptibility χm = 6 in a given region as B = 0.005 y^2 ax T. Find the magnitude of current density J at y = 0.4 m.
The internal inductance of a straight wire of circular cross-section with radius r, length l and permeability µ is
Determine the energy density in free space created by a magnetic field with intensity H = 10^3 A/m.
A triangle defined by A(2, -5, 1), B(0, 2, 4) and C(0, 3, 1). What is area of the triangle?
A 2 mC positive charge is located in vacuum at point P1(3, -2, -4) and 5 µC negative charge is located at P2(1, -4, 2). What is the magnitude of force on the charge at P1?
Four infinite uniform sheets of charges with following uniform charge density are placed at different points in space as following : Sheet-1 : 20 pC/m^2 at y = 7; Sheet-2 : -8 pC/m^2 at y = 3; Sheet-3 : 6 pC/m^2 at y = -1; Sheet-4 : -18 pC/m^2 at y = -4. Find the magnitude of Electric field E at point P(2, 6, -4). Consider relative permittivity of the medium as 1.
A 25 µC point charge is located at origin. Calculate electric flux passing through the portion of sphere defined by r = 20 cm, bounded by θ = 0 and π rad, φ = 0 and π/2 rad.
A dielectric material is placed in vacuum in a uniform electric field of E = 4 V/m. What is the electric field inside the material if the relative permittivity of dielectric material is 2?
Find the relative permittivity of dielectric material used in a parallel plate capacitor if electric flux density D = 15 µC/m^2 and energy density is 20 J/m^3.
For a homogeneous medium with volume charge density ρv, permittivity ε and voltage V. What is the ∇²V ?
Which among the following equation is true for a steady magnetic field? Where B is magnetic flux density, J is current density and H is magnetic field intensity.
An electron beam carries a total current of -500 µA in the az direction and has a current density Jz in the region 0 ≤ r ≤ 10^-4 m and zero in the region r > 10^-4 m. Electron beam velocity is given by Vz = (8 × 10^7 z) m/s. Calculate the volume charge density at z = 2 cm.
Find the magnitude of the electric field intensity in a sample of silver having conductivity σ = 6.17 × 10^7 mho/m, permittivity µe = 0.006 m^2/Vs and drift velocity 1 mm/s.
Which among the following statement is correct regarding an ideal conductor in a static electric field?
Consider electron and hole mobilities of germanium at 300K is 0.36 m^2/Vs and 0.17 m^2/Vs respectively and hole and electron concentration of 2.7 × 10^19 per m^3. Find the conductivity of germanium at 300 K.
The technology 'CMOS' used for fabricating integrated circuit refers to
A 3 phase, 50 Hz synchronous generator is connected to an infinite bus. The maximum power that can be transferred to infinite bus is 1 p.u. The mechanical input to the generator is √3/2 p.u. Inertia constant of the generator is 5s. Find the natural frequency of oscillation of the system?
A 3 phase, 50 Hz synchronous generator is connected to an infinite bus through a transformer and two parallel transmission lines. The input mechanical power to synchronous generator is 0.8 p.u. Grid is consuming a power of 0.8 + j0.4 p.u., generator impedance is 0.25 p.u., transformer impedance is 0.5 p.u. and each transmission line impedance is 0.5 p.u. If the infinite bus voltage is 1∠0 p.u. then, what is the generator voltage load angle? [Figure description (from the worked solution): single-line diagram of a generator (Pm = 0.8, reactance j0.25) feeding a transformer (j0.5) and then two parallel transmission lines (j0.5 each) to the infinite bus 1∠0° p.u., where a load of 0.8 + j0.4 is connected.]
Which is the power semiconductor device having highest switching speed?
For a PN junction diode, width of space charge region increases as?
If unit step response of a network is (1 - e^(-αt)) then its unit impulse response will be
What is the Laplace transform of function δ(t - 2)?
What is the range of 'K' for which the unity feedback closed loop system with open loop gain G(s) = K / (s^2 (s + a)) will be unstable?
A power supply having output resistance 1.5 Ω supplies a full load current of 500 mA to a 50 Ω load. Determine the percentage voltage regulation of supply?
Find the voltage VN for the circuit shown below? [Figure description: An op-amp circuit. A 40 kΩ resistor is connected from ground to node V1, which connects to the inverting (-) input; a 6 V source (polarity marked - + ) is connected between node V1 and the op-amp output V0. The non-inverting (+) input node VN is connected to ground through a 10 kΩ resistor and to the output V0 through a 20 kΩ resistor.]
The integral (1/2π) ∫ from 0 to 2π of sin(t - τ) cos τ dτ equals to
If u(t), r(t) denote unit step and unit ramp respectively and u(t)*r(t) their convolution, then function u(t + 1) * r(t - 2) is
Consider function f(x) = (x^2 - 4)^2, where x is a real number. The function f(x) has
A is an (m × n) matrix with m > n and 'I' is identity matrix. Let A1 = (A^T A)^-1 A^T, then which of the following statement is false?
For the circuit diagram shown below, calculate the voltage across capacitor V(t) at t = 160 µs? [Figure description: A single-loop circuit. A 50 V DC source (+ at top) in series with a 70 Ω resistor and a switch (closing/opening at t = 0) in the top wire; an 80 Ω resistor on the left vertical branch in parallel with a 2 µF capacitor (voltage v, + on top) in the middle vertical branch.]
Consider a parallel RLC circuit having inductance of 10 mH, capacitance of 100 µF. Determine the value of resistance that would lead to a critically damped response?
A power BJT has collector current IC = 20 A at IB = 2.5 A and reverse saturation current ICS = 15 mA. Find out current gain β?
One cycle of square wave signal observed on an oscilloscope is found to occupy 6 cm at a scale setting of 30 µs/cm. What is the signal frequency?
Two equal voltages of same frequency applied to X and Y plates of CRO produce a circle on the screen. The phase difference between the two voltages will be?
The magnetic field intensity of uniform plane wave in air is 20 A/m in the direction ay. The wave is propagating in the az direction at a frequency of 2 × 10^9 rad/s. What is the wave length of the plane wave.
A loss less transmission line segment has characteristic impedance Z0 = 100 Ω electromagnetic wave propagation velocity in the transmission line v = 0.8 times velocity of light in vacuum. The frequency of the electromagnetic wave transmitted is 100 MHz. The phase constant is β and βl = π rad, then what is the length of the transmission line segment l ?
A 100 pF capacitor has a maximum charging current of 150 µA. What is the slew rate of capacitor?
An operational amplifier has a time rate of change of voltage of 2 V/µs. If the peak output voltage is 12 V, what is the bandwidth of the amplifier?
A 10 kVA, 200 V/2000 V transformer is feeding a load resistance of 2.5 p.u. based on ratings of HV side. The actual value of load resistance referred to LV side?
While performing short circuit test on a single-phase 110/220 V, 50 Hz transformer with LV side shorted, wattmeter reading is found to be 20 W. If the same test is performed on the transformer with HV side shorted, the wattmeter reading will be?
For a 3-phase slip-ring induction motor, the electrical rotor losses are proportional to
The blocked-rotor test of squirrel-cage induction motor determines?
Which among the following statement is true for a power system with lagging power factor?
What is the volume charge density at point P(1, 2, 1) associated with electric flux field D = xy^2 ax + yx^2 ay + z az C/m^2.
An electric Field is given by E = zy^2 ax + 2xyz ay + xy^2 az V/m, an incremental path is represented by ΔL = -3ax + 5ay - 2az µm. Find the work done in moving 4 µC charge along the incremental path if the location of the path is at point P(1, 1, 1).
Assuming zero voltage at infinity, find the potential at P(0, 0, 10) that is caused by a charge distribution of 10 nC/m along the line x = 0, y = 0, -1 < z > 1 in free space.
A point charge of +3 µC and -3 µC are located at (0, 0, 1) and (0, 0, -1) respectively, in free space. Find the magnitude of dipole moment. Consider distances in meters.
In the circuit shown below, steady state was reached when the switch 's' was open. The switch was closed at t = 0. The initial value of the current through the capacitor 2 C is [Figure description: An 18 V source on the left in series with a 2 Ω resistor along the top wire. After the 2 Ω resistor, the circuit has two parallel branches: (1) a branch with a 4 Ω resistor in series with an inductor L down to the bottom wire, and (2) a branch of two capacitors in series (2 C on top, C below) down to the bottom wire. A switch s connects the midpoint between 4 Ω and L to the midpoint between the capacitors 2 C and C.]
The Laplace transform of (t^2 - 2t) u(t - 1) is?
A source Vs = 200 cos ωt delivers power to a load at power factor 0.8 lag. The reactive power is 300 VAR. The Active Power is given by?
An ideal constant current source is connected in series with an ideal constant voltage source. Considering both together the combination will be a?
Calculate Ceq of the circuit given below? [Figure description: A capacitor network between two terminals (left). From the upper terminal: a 7 F capacitor in series, to a node; from this node a 5 F capacitor goes down to the lower rail (shunt, Ceq looks in at the left of this). From the node, a 4 F capacitor runs along the top to a second node. From this second node: a series pair of 8 F (top) and 5 F (bottom) capacitors goes down to the second bottom node; further right, a branch of 2 F (top), 12 F (right vertical) and 2 F (bottom) capacitors in series connects the second top node around to the second bottom node. The bottom rail has a 1 F capacitor in series between the first bottom node and the second bottom node.]
The voltage across 2H inductor is 6 cos(5t) V. Determine the resulting inductor current at t = π, if the inductor current at t = -π/2 is 1 A?
Given the points A(x = 2, y = 3, z = -1) and B(r = 4, θ = 30°, φ = 120°). Find distance between A and B.
A synchronous motor is operating at constant load, while its excitation is adjusted to get unity power factor. If the excitation is now increased, the power factor will be?
If the positive, negative and zero-sequence reactances of an element of a power system are 0.3, 0.3 and 0.8 p.u. respectively, then the element would be a?
A 100 MW power station delivers 100 MW for 2 hours, 50 MW for 6 hours in a day and is shut down for maintenance for 45 days each year. Calculate its annual load factor?
Determine the inductor voltage 'V' in the circuit shown below for t > 0? [Figure description: A 6 Ω resistor on the left vertical branch; a 10 V battery in the middle vertical branch with a switch (t = 0) above it; on the right, a 4 Ω resistor in the top wire in series with a 5 H inductor (voltage v, + on top, current iL downward). The battery, 6 Ω resistor and the 4 Ω + inductor branch share top and bottom rails; the switch is in series with the battery.]