For a given vector , the vector normal to the plane defined by is
Equation of plane in 3D:
Vector normal to plane is given by
For the block diagram shown in the figure, the transfer function is
Various signals in block diagram are marked below
Transfer Function
In the Nyquist plot of the open-loop transfer function
Corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at
Nyquist contour:
Infinite semicircular arc: S =
θ: to –
G (s) H (s) =
=
Consider a unity-gain negative feedback system consisting of the plant (s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, are
Transfer function of PI controller
Given, &
Block Diagram of Control System is given by
Forward path transfer function
Overall transfer function
Final value of plant output,
Controller Output X(s) =
X(s) =
Final value of controller
The following columns present various modes of induction machine operation and the ranges of slip
(A) Mode of Operation | (B) Range of Slip |
(a) Running in generator mode | (p) From 0.0 to 1.0 |
(b) Running in motor mode | (q) From 1.0 to 2.0 |
(c) Plugging in motor mode | (r) From -1.0 to 0.0 |
The correct matching between the elements in column A with those of column B is
a-r, b-p, and
a-r, b-q, and c-p
, and
a-q, b-p, and c-r
Torque-slip characteristics of Induction machine are shown below.
A 10-pole, , single phase induction motor runs at while driving rated load. The frequency of induced rotor currents due to backward field is
Synchronous speed,
Since, rotor rotates opposite to backward field
Sup,
Rotor induced frequency due to backward field
= sf = 1.9 × 50 = 95 Hz
A continuous-time system that is initially at rest is described by
where is the input voltage and is the output voltage. The impulse response of the system is
Differential equation of system is,
Take Laplace Transform both sides
sY(s) + 3Y(s) = 2X(s)
Transfer Response,
The Fourier transform of the signal is given by
Which one of the following statements is true?
tends to be an impulse as .
decreases as increases.
At
At
Fourier Transform is
Option a: As , rectangular pulse becomes a constant function X(ω) = 1
Option (a) is correct
Option (b) :
x(0) increases as increases
option (b) is incorrect
option C: ]
Option (c) as well as (d) are incorrect
The Z-transform of a discrete signal is
Which one of the following statements is true?
Discrete-time Fourier transform of converges if is
Discrete-time Fourier transform of converges if is
Discrete-time Fourier transform of converges if is such that is a left-sided sequence
Discrete-time Fourier transform of converges if is such that is a rightsided sequence
Based on pole location, there are 4 possible ROCs
ROC-1 : ∴ |Z| < 1/5, x[n] is a left-sided sequence unit circle does not lie in this ROC : DTFT does not converge.
ROC-2:
Unit circle does not lie in this ROC ∴ DTFT does not converge.
ROC – 3:
Unit circle lies in this ROC ∴DTFT converges
ROC-4: |Z| > 3, x[n] is a right-sided sequence unit circle does not lie in this ROC ∴ DTFT does not converges.
For the three-bus power system shown in the figure, the trip signals to the circuit breakers to are provided by overcurrent relays to , respectively, some of which have directional properties also. The necessary condition for the system to be protected for short circuit fault at any part of the system between bus 1 and the - loads with isolation of minimum portion of the network using minimum number of directional relays is
and are directional overcurrent relays blocking faults towards bus 2.
and are directional overcurrent relays blocking faults towards bus 2 and is directional overcurrent relay blocking faults towards bus 3.
and are directional overcurrent relays blocking faults towards Line 1 and Line 2, respectively, is directional overcurrent relay blocking faults towards ine 3 and is directional overcurrent relay blocking faults towards bus 2.
and are directional overcurrent relays blocking faults towards Line 1 and Line 2, respectively.
Directional relays are used at load end of interconnected line or ring mains.
We must always connect directional relay at location where current may reverse in event of a fault.
Based on above concept, the position of directional & non-directional relays are shown below.
↔ : non-directional relay
← : directional relay
& are directional relays that trip for faults towards Line-1 & Line-2 respectively.
Also, & block fault towards Bus-2.
The expressions of fuel cost of two thermal generating units as a function of the respective power generation and are given as:
where is a constant. For a given value of , optimal dispatch requires the total load of to be shared as and . With the load remaining unchanged, the value of is increased by and optimal dispatch is carried out. The changes in and the total cost of generation, in Rs/hour will be as follows:
will decrease and will increase.
Both and will increase.
will increase and will decrease.
Both and will decrease.
If a is increased by 10% the slope of incremental cost of generator 1 increases so for economic load dispatch when IC1=IC2
Pa1 reduces & Pa2 increases
As a increases & Pa1 reduces there is slight change in F1
As Pa2 increases, F2 increase
∴ Overall cost F1 + F2 increases
The four stator conductors and of a rotating machine are carrying currents of the same value, the directions of which are shown in the figure (i). The rotor coils - ' and - ' are formed by connecting the back ends of conductors ' ' and ' ' and ' ' and ' ', respectively, as shown in figure (ii). The e.m.f. induced in coil - ' and coil - are denoted by and , respectively. If the rotor is rotated at uniform angular speed in the clockwise direction then which of the following correctly describes the and ?
fig. (i) cross-section view fig. (ii) rotor winding connection diagram
and have finite magnitudes and are in the same phase.
and , have finite magnitudes with leading
and have finite magnitudes with leading
Magnetic field produced by stator is shown below
The poles formed on stator based on direction of magnetic field are also shown.
Number of poles = 4
If θe = 90°, θm = 45°
Geometry Neutral Axis (GNA) lies at 90° electrical to pole axis ie. at 45° mechanical to poles axis. GNA is shown in figure below.
Since the coils a-a’ & b-b’ lie along GNA, emf induced in each of them is 0.
The chopper circuit shown in figure (i) feeds power to a 5 A DC constant current source. The switching frequency of the chopper is . All the components can be assumed to be ideal. The gate signals of switches and are shown in figure (ii). Average voltage across the 5 A current source is
Fig. (i)
Fig. (ii)
Since the load is a constant current source only devices S1 & D2 can conduct based on current direction.
When S1 is ON
V0=20 V
When S1 is off D2 turns ON
V0=0
Based on switching signal waveform
S1 conducts from 0 to 3μs V0 = 20
D2 conducts from 3μs to 10μs V0 = 0
∴ average output voltage
V0 (avg) = 6 volt
In the figure, the vectors and are related as: by a transformation matrix A. The correct choice of is
is CW rotation of by 36.86°
For rotation of a vector by an angle θ in anti-CW direction matrix used.
When vector is to be rotated CW, we use negative value of θ.
θ = -36.86°, cos θ = 0.8, sin θ = -0.6
matrix
One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation .
The is estimated by randomly drawing out 10,000 numbers of samples . The estimates are computed in the following two ways.
Since, there are 1 million random number but we are selecting 10000 random numbers out of 1 million. Hence. standard deviation is called Sample Standard Deviation.
Sample Variance for N samples
For 0 mean & 10000 samples
A semiconductor switch needs to block voltage of only one polarity during OFF state as shown in figure (i) and carry current in both directions during ON state as shown in figure (ii). Which of the following switch combination(s) will realize the same?
Fig. (i)
Fig. (ii)
Since, the switch can block only one polarity of voltage called as Unipolar Switch.
But, since current can flow in both directions, so the switch is bidirectional.
Whenever anti-parallel diode is connected to a switch then reverse current can also flow so switch becomes Bidirectional.
as shown current can flow in both directions.
BJT blocks forward voltage but diode cannot allow blocking reverse voltage.
Switch is unipolar & bidirectional.
Diode connected in series does not allow current flow in both directions.
BJT blocks forward voltage while series diode blocks reverse voltage
∴ switch is unidirectional & bipolar.
Diode connected in series does not allow current flow in both directions.
BJT blocks forward voltage & series diode blocks reverse voltage. hence switch is unipolar.
∴ switch is bipolar & unidirectional
This switch is combination of previous switch & antiparallel diode.
∴ switch becomes bidirectional & unipolar.
Which of the following statement(s) is/are true?
If an LTI system is causal, it is stable.
A discrete time LTI system is causal if and only if its response to a step input is 0 for .
If a discrete time system has an impulse response of finite duration the system is stable.
If the impulse response for all , then the LTI system is stable.
(a) for a causal LTI system, h[n] = 0 ∀ n < 0 & for stability
∴ Causal LTI system may or may not be stable.
(b) for causal LTI system, h[n] = 0 ∀ n < 0
Step response, s[n] = u[n] * h[n]
∴ both u[n] & h[n] = 0 ∀ n < 0
∴ S[n] = 0 ∀ n < 0
(c) if h[n] has finite duration, then system may or may not be stable
Has finite duration but h[n] is not absolutely summable ∴ system is unstable.
(d) if 0 < |h[n]| < 1 then system may be unstable because if signal has infinite duration then h[n] is not absolutely summable.
The bus admittance matrix of a 3-bus power system is given below.
Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT be true?
Sum of the elements in a row of YBUS matrix represents the admittance b/w particular bus & ground.
Based on values above the system can be represented as,
π-model of a transmission line can be shown as
That is the line has equal capacitances at both ends.
So, we can consider line connecting bus-2 & 3 only has line charging capacitance of j0.5
Bus-3 has shunt capacitor of j0.5
∴ Statement b & d are correct & statement a & c are incorrect.
The value of parameters of the circuit shown in the figure are :
For time , the circuit is at steady state with the switch ' ' in closed condition. If the switch is opened at , the value of the voltage across the inductor at in Volts is ________ (Round off to 1 decimal place).
Since the switch was closed for a long time before t = 0 circuit is in steady state at
∴ L is short circuited & C is open circuited
At t = 0+ S is opened & inductor is replaced by a current source & capacitor is replaced by a voltage source.
By KCL, current in capacitor branch = 4A
By KVL, 6R1 + VL = 4R2 + 12
VL = 4 × 2 – 6 × 2 + 12 = 8 volt
A separately excited DC motor rated A, 1500 RPM drives a constant torque load at rated speed operating from supply drawing rated current. The armature resistance is 1.2Ω . If the supply voltage drops by with field current unaltered then the resultant speed of the motor in RPM is __________ (Round off to the nearest integer).
Load to constant torque T = constant
Under rated condition
E1 = Vt – Iara = 400 – 15 × 1.2 = 382 V
Since motor is separately excited φ = constant
When supply voltage is reduced by 10%
∴ T = constant
if φ = constant Ia = constant for constant torque
∴ Ia = 15A
N2 = 1343 rpm
For the signals shown in the figure, is maximum at . Then in seconds is __________ (Round off to the nearest integer).
For maximum value of convolution we must have maximum area under product of x(t - τ) & y(τ).
∴ (t – 1) must coincide with t = 3 so that entire positive area under y(t) coincide with x(t - τ)
∴ t – 1 = 3
t = 4
∴ z(t) = max occurs at t = 4
For the circuit shown in the figure, and . The voltage in Volts is __________ (Round off to 1 decimal place).
Assume node-b as reference & applying nodal analysis.
8V – 48 = 0
V = 6 Volt
A line of length has the following parameters:
Resistance,
Inductance, ;
Capacitance,
The line is represented by the nominal- model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by and , respectively) maintained at , the phase angle difference between and required for maximum possible active power to be delivered to the receiving end, in degree is ________ (Round off to 2 decimal places).
The expression for active power delivered to receiving end is,
For maximum value of PR
Phase shift b/w Vs & VR δ = β
For nominal π-model, ABCD parameter are given by
L = 1 mH/km × 400 km = 400 mH = 0.4 H
R = 0.035 Ω/Km × 400 km = 14Ω
In the following differential equation, the numerically obtained value of , at , is __________ (Round off to 2 decimal places).
y(0) = 0 y(1) = ?
h = 1 (step size)
y(1) = y(0) + hf(0, 0)
Three points in the -y plane are and . The value of the slope of the best fit straight line in the least square sense is __________ (Round off to 2 decimal places).
x | y |
-1 | 0.8 |
0 | 2.2 |
1 | 2.8 |
Mean of x co-ordinates
Mean of y co-ordinates
Slope of least square fit line
m = 1
The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is
Magnitude of gain = 8dB = 20 log K
Phase is linear & at
Or rad at ω = 1
∴ Slope of phase plot
So, transfer function can be expressed as
Consider the OP AMP based circuit shown in the figure. Ignore the conduction drops of diodes and . All the components are ideal and the breakdown voltage of the Zener is . Which of the following statements is true?
The maximum and minimum values of the output voltage are and , respectively.
The maximum and minimum values of the output voltage are and , respectively.
The maximum and minimum values of the output voltage are and , respectively.
The maximum and minimum values of the output voltage are and , respectively.
Applying open circuit test
Due to absence of feedback op-amp acts as comparator
V+ = 0 V- = VIN
during +ve half cycle VIN > 0 V- > V+
V0 = -VSAT
D1 & zener diode are forward biased & D2 is reverse biased
During -ve half cycle VIN < 0 V- < V+
V0 = VSAT = 15V
D2 is forward biased & D1 & Zener diode are reverse biased
Zener diode goes into BD.
During +ve half cycle
∴ minimum value of V0 = -10V
During -ve half cycle
∴ Maximum value of V0 = 5Volt
Consider a lead compensator of the form
The frequency at which this compensator produces maximum phase lead is . At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of , is . The values of , respectively, are
1,16
2,4
3,5
Frequency of maximum phase shift
Corner frequencies = α, αβ
At frequency of maximum phase shift,
Asymptotic approximation of K(s) is,
A 3-phase, star-connected, balanced load is supplied from a 3-phase, (rms), balanced voltage source with phase sequence R-Y-B, as shown in the figure. If the wattmeter reading is and the line current is (rms), then the power factor of the load per phase is
Wattmeter is connected such that current coil lies in one phase & potential coil is connected across other 2 phases.
Reading of wattmeter = VLIL sinφ
-400 = 400 × 2 × sinφ
φ = -30°
Since φ < 0, pf is leading
pf = cos 30° = 0.866 leading
An 8-bit ADC converts analog voltage in the range of 0 to to the corresponding digital code as per the conversion characteristics shown in figure. For , which of the following digital output, given in hex, is true?
length of each interval or step size = 19.6 mV
Number of steps for given analog input
= 101.64
∴ The o/p makes a transition at middle of interval as can be seen from graph.
& 101.64 > 101.5 ∴ output will be hexadecimal value of 102
(102)10 = (66)H
The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is infinite bus having a voltage of magnitude p.u. and angle of . A variable current source, is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at
1.05 p.u. and the phase angle of the source current, , where is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as
Bus 1 Slack Bus
Bus Bus
Bus Bus
Bus Bus
Bus Bus
Bus Bus
Bus 3 Slack Bus
Bus Bus
Bus Bus
Bus 3 Slack Bus
Bus Bus
Bus 3 Slack Bus
Since voltage magnitude is given at bus 1 & angle of current source
∴ Phase shift b/w V & I across current source =
∴ P = 0, Hence Bus – 1 is PV bus
Bus-2 has real & reactive power specified ∴ it can be characterized as PQ bus.
Bus-3 has voltage magnitude & phase angle specified
∴ It can be characterized as slack bus.
Consider the following equation in a 2-D real-space.
Which of the following statement(s) is/are true.
When , the area enclosed by the curve is .
When tends to , the area enclosed by the curve tends to 4.
When tends to 0, the area enclosed by the curve is 1.
When , the area enclosed by the curve is 2.
(a) if p = 2
Equation
This equation represents a circle of radius = 1
(b) if p → ∞ then x1 & x2 ≤ 1 else if any of these values is > 1 then or so sum cannot be 1
If |x1| < 1 ∴ |x2| = 1 for sum to be 1
If |x2| < 1 ∴ |x1| = 1 for sum to be 1
The shape looks like as shown below,
(c) if then non-zero values of &
Sum = 2
Hence if x1 ≠ 0 x2 must be zero & vice versa so curve looks like as shown below,
No closed curve exists & area = 0
(d) if P = 1, equation becomes |x1| + |x2| = 1
Curve looks like as shown below
In the figure, the electric field and the magnetic field point to and directions, respectively, and have constant magnitudes. A positive charge ' ' is released from rest at the origin. Which of the following statement(s) is/are true.
The charge will move in the direction of with constant velocity.
The charge will always move on the plane only.
The trajectory of the charge will be a circle.
The charge will progress in the direction of .
MTA
All the elements in the circuit shown in the following figure are ideal. Which of the following statements is/are true?
When switch is , both and conducts and is reverse biased.
When switch is conducts and both and are reverse biased.
When switch is OFF, is reverse biased and both and conduct.
When switch is OFF, conducts, is reverse biased and conducts.
When S is ON, diode D3 gets reverse biased
Assume D1 is ON & D2 is OFF
I1 = 4A > 0 ∴D1 is ON
VD2 = -20 V < 0 ∴D2 is OFF
∴ Option (b) is correct
When S is OFF, D3 is ON due to 2A current source Assume D1 is OFF & D2 is ON
ID2 = 4A > 0 ∴ D2 is ON
VD1 = 20 – 40 = -20 < 0 ∴D1 is OFF
∴ Option (c) is correct
The expected number of trials for first occurrence of a "head" in a biased coin is known to be 4. The probability of first occurrence of a "head" in the second trial is __________ (Round off to 3 decimal places).
∴ Coin is biased
If P (Head) = p then P(Tail) = 1 – p = q
Assume head occurs for first time on trial
For other (n-1) trial Tail must appear
Consider the state-space description of an LTI system with matrices
For the input, , the value of for which the steady-state output of the system will be zero, is __________ (Round off to the nearest integer).
Transfer Function is given by,
A three-phase synchronous motor with synchronous impedance of per unit per phase has a static stability limit of 2.5 per unit. The corresponding excitation voltage in per unit is _________(Round off to 2 decimal places).
Developed power of a Synchronous Motor,
Motor is stable if
Steady state stability Limit
Assume Vt =1pu
Ef = 1.5811 pu
A three phase , 6-pole, squirrel cage induction motor drives a constant torque load at rated speed operating from rated supply and delivering rated output. If the supply voltage and frequency are reduced by , the resultant speed of the motor in RPM (neglecting the stator leakage impedance and rotational losses) is _________ (Round off to the nearest integer).
if both voltage & frequency are reduced by 20% then
Motor drives a constant Torque Load, Ns – Nr = constant f1 = 50 Hz
Ns1 – Nr1 = Ns2 – Nr2
1000 – 960 = 800 – Nr2
Nr2 = 760 rpm
The period of the discrete-time signal described by the equation below is __________ (Round off to the nearest integer).
Period of
Period of
= rational ∴ overall signal is periodic
N = LCM (N1, N2) = LCM (16, 6) = 48
The discrete-time Fourier transform of a signal is . Consider that is a periodic signal of period such that
Note that . The magnitude of the Fourier series coefficient is __________ (Round off to 3 decimal places).
,
For the circuit shown, if , the instantaneous value of the Thevenin's equivalent voltage (in Volts) across the terminals at time is __________ (Round off to 2 decimal places).
Applying nodal analysis to super node
∴ v(t) = 12.5 sin (1000t)
At t = 5 msec v(t) = 12.5 sin 5 = -11.986
The admittance parameters of the passive resistive two-port network shown in the figure are :
The power delivered to the load resistor in Watt is ________ (Round off to 2 decimal places).
Based on given y-parameters of 2 port network
y11 = 5 y22 = 1 y12 = y21 = -2.55
We can represent 2-port network as π-model
Connecting this model to given circuit
Applying KCL at node voltage V
18 V = 680;
When the winding of the single-phase, , two winding transformer is supplied from an AC current source of frequency , the rated voltage of (rms), is obtained at the open-circuited terminals . The cross sectional area of the core is and the average core length traversed by the mutual flux is . The maximum allowable flux density in the core is and the relative permeability of the core material is 5000. The leakage impedance of the winding and winding at are and , respectively. Considering the magnetizing characteristics to be linear and neglecting core loss, the self-inductance of the winding a-b in millihenry is _________ (Round off to 1 decimal place).
Open circuit voltage at a-b = 200V (rms)
Reluctance of flux path inside core =
Mutual inductance referred to primary =
Self inductance of primary = M + Lep
= 2.0357 + 0.16 = 2.1957
= 2195.7 mH
The circuit shown in the figure is initially in the steady state with the switch in open condition and in closed condition. The switch is closed and is opened simultaneously at the instant , where . The minimum value of in milliseconds, such that there is no transient in the voltage across the capacitor, is (Round off to 2 decimal places).
Before t = t1 Kcs open & is closed & circuit reaches steady state
The current of 5V dc source keeps circulating in a loop & does not affect capacitor.
at t = t1,
after t = t1 k closed so ac current source is shorted & is open so a series RC circuit with 5V dc source is formed.
Initial capacitor voltage
Steady state capacitor voltage = 5V
Second term represents transient
For transient-free response
The circuit shown in the figure has reached steady state with thyristor '' in OFF condition. Assume that the latching and holding currents of the thyristor are zero. The thyristor is turned at . The duration in microseconds for which the thyristor would conduct, before it turns off, is ___ (Round off to 2 decimal places).
If circuit is in steady state with T : OFF
C : Open L : shoot
vc = 100V iL = 0A
Now when T : ON, a LC oscillator is formed
Load current
= 25 + 50 sinω0t
T turns OFF when IT = 0
25 + 50 sinω0t = 0
Neglecting the delays due to the logic gates in the circuit shown in figure, the decimal equivalent of the binary sequence of initial logic states, which will not change with clock, is
Assume initial state of circuit Q1 Q2 = 00
Characteristic equation of D-flip flop: Qn+1 = D
Q2(n+1) = C = Q1
For binary sequence [ABCD] to remain same, state of circuit must remain same
Q1 | Q2 | Q1(n+1) | Q2(n+1) |
0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 1 |
∴ When Q1 Q2 = 00, next state is same as present state & hence binary sequence remains same.
C = Q1 = 0
[ABCD] = [1000]
Decimal value = 8
In a given 8-bit general purpose micro-controller there are following flags. C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity (0 for even, 1 for odd) and are the two general purpose registers of the micro-controller. After execution of the following instructions, the decimal equivalent of the binary sequence of the flag pattern [CAOP] will be
MOV RO,
MOV R1, +0x46
ADD R0, R1
MOV R0, 0 × 60 ← (60)H is stored in R0
MOV R1, 0 × 46 ← (46)H is stored in R1
ADD R0, R1
Both values get added
Number of 1’s in result = 4 = even ∴ P =0
Overflow bit is 1 because both numbers have MSB = 0 i.e. positive numbers but result has MSB = 1 i.e. negative number.
CAOP = 0010; decimal value = 2
The single phase rectifier consisting of three thyristors and a diode feed power to a constant current load. and are fired at α=60° and is fired at α=240° . The reference for is the positive zero crossing of . The average voltage across the load in volts is ________ (Round off to 2 decimal places).
Since the load carries constant current one device out of T1 & D1 must always be conducting & one out of T2 T3 most always be conducting
T1 : α to π i.e. 60° to 180°
D1: π to 2π + α i.e. 180° to 360° & 0° to 60°
T2: π + α to 2π + α i.e. 240° to 240°
T3: α to π + α i.e. 60° to 240°
∴ Output voltage is
0 to 60° : D1 & T2 : ON V0 = -Vs
60° to 180° : T1 & T3 : ON V0 = Vs
180° to 240° : T3 & D1 : ON V0 = 0
240° to 360° : T2 & D1 : ON V0 = -Vs
The Zener diode in circuit has a breakdown voltage of . The current gain of the transistor in the active region in 99. Ignore base-emitter voltage drop . The current through the 20Ω resistance in milliamperes is _________ (Round off to 2 decimal places).
Apply OC Test on Zener diode
Given VBE = 0
25 – 7000 IB – 0 – 10IE – 20IE = 0
25 = 100 IE ∴IE = 0.25A = 250 mA
By KVL: -VD – 0 – IE × 10 = 0
VD = -2.5 V
Zener diode is reverse biased but does not operate in breakdown region & hence open.
The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a - transformer. The positive, negative and zero-sequence diagrams of the system are shown in figures (ii), (iii) and (iv), respectively. All reactances in the sequence diagrams are in p.u. For a bolted line-to-line fault (fault impedance = zero) between phases ' ' and ' ' at bus 1 , neglecting all pre-fault currents, the magnitude of the fault current (from phase ' ' to ' ') in p.u. is _______ (Round off to 2 decimal places).
Fig. (i) : Single-line diagram of the power system
Fig. (iii) : Negative-sequence network Fig. (ii) : Positive-sequence network
Fig. (iv) : Zero-sequence network
Since a L-L fault occurs at bus-1
We need Thevenin Impedance for all 3 sequence at bus-1
An infinite surface of linear current density exists on the plane, as shown in the figure. The magnitude of the magnetic field intensity at a point due to the surface current in Ampere/meter is __________ (Round off to 2 decimal places).
Magnetic field intensity due to surface current density kA/m is
The closed curve shown in the figure is described by , where ;
. The magnitude of the line integral of the vector field around the closed curve is __________ (Round off to 2 decimal places).
x = r cosθ dx = -r sinθdθ
y = r sin θ dy = r cos θ dθ
on closed curve
A signal is sampled at and then passed through an ideal low pass filter having cut-off frequency of . The maximum frequency present in the filtered signal in is __________ (Round off to the nearest integer).
X(t) = 2 cos (180 πt) cos (60πt)
=cos (240 πt) + cos (120 πt)
So, spectrum of x(t) contains impulses at following frequencies: -120, 120, -60, 60
Due to sampling spectrum shifts by nfs
fs = sampling frequency = 200 Hz
n = 0 components: - 60, -120, 80, 120
n = 1 components: 140, 80, 260, 320
n = 2 components: 340, 280, 460, 520
∴ the sampled signal is passed through a LPF with cut off frequency = 100 Hz highest frequency passing through filters = 80 Hz
A balanced delta connected load consisting of the series connection of one resistor (R=15Ω) and a capacitor in each phase is connected to three-phase, supply terminals through a line having an inductance of per phase, as shown in the figure. Considering the change in the supply terminal voltage with loading to be negligible, the magnitude of the voltage across the terminals in Volts is ________ (Round off to the nearest integer).
Convert Δ connected load to star
By this conversion phase voltage across load changes but line voltage remains same
By voltage division
Magnitude of load voltage per phase
Line to line voltage across load = 415 V
A quadratic function of two variables is given as
The magnitude of the maximum rate of change of the function at the point is ________ (Round off to the nearest integer).
Maximum rate of change is given by Gradient
As (1, 1),
