The $$i$$-v characteristics of the diode in the circuit given below are $$$i = \left\{ {\matrix{ {{{v - 0.7} \over {500}}A,} & {v \ge 0.7\,V} \cr {0A,} & {v < 0.7\,V} \cr } } \right.$$$

The current in the circuit is

The voltage gain $${A_V}$$ of the circuit shown below is

The circuit shown is a

The feedback system shown below oscillates at $$2$$ rad/s when

A system with transfer function $$\,G\left( s \right) = {{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \right)\left( {s + 3} \right)\left( {s + 4} \right)}}$$ is excited by $$\sin \left( {\omega t} \right).$$ The steady-state output of the system is zero at

The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$

$${G_c}\left( s \right)$$ is a lead compensator if

The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$

The phase of the above lead compensator is maximum at

The state variable description of an $$LTI$$ system is given by $$$\left( {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr {\mathop {{x_3}}\limits^ \bullet } \cr } } \right) = \left( {\matrix{ 0 & {{a_1}} & 0 \cr 0 & 0 & {{a_2}} \cr {{a_3}} & 0 & 0 \cr } } \right)\left( {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right) + \left( {\matrix{ 0 \cr 0 \cr 1 \cr } } \right)u,$$$ $$$y = \left( {\matrix{ 1 & 0 & 0 \cr } } \right)\left( {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right)$$$

where $$y$$ is the output and $$u$$ is the input. The system is controllable for

In the sum of products function $$f\,\left( {X,\,Y,\,Z} \right) = \sum \left( {2,\,\,3,\,\,4,\,\,5} \right),$$ the prime implicants are

The output $$Y$$ of a $$2$$ $$-$$ bit comparator is logic $$1$$ whenever the $$2$$-bit input $$A$$ is greater than the $$2$$-bit input $$B.$$ The number of combination for which the output is logic $$1$$, is

Consider the given circuit. In this circuit, the race around

The state transition diagram for the logic circuit shown is

In the circuit shown below, the current through the inductor is

If $$V_A-V_B=\;6\;V$$, then $$V_C-V_D$$ is

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

In the following figure, C₁ and C₂ are ideal capacitors. C₁ has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is

The average power delivered to an impedance $$\left(4-j3\right)$$ Ω by a current $$5\cos\left(100\mathrm{πt}+100\right)\;A$$ is

A two phase load draws the following phase currents: $$i_1\left(t\right)=I_m\sin\left(\omega t-\phi_1\right)$$, $$i_2\left(t\right)=I_m\cos\left(\omega t-\phi_2\right)$$. These currents are balanced if $$\phi_1$$ is equal to

In the circuit shown, the three voltmeter readings are V₁ = 220V, V₂ = 122V , V₃ = 136V. The power factor of the load is

In the circuit shown, the three voltmeter readings are V₁ = 220V, V₂ = 122V , V₃ = 136V. If R_L=5 Ω , the approximate power consumption in the load is

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:

(i) 1 Ω connected at port B draws a current of 3 A
(ii) 2.5 Ω connected at port B draws a current of 2 A

W ith 10 V dc connected at port A, the current drawn by 7 Ω connected at port B is

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:

(i) 1 Ω connected at port B draws a current of 3 A
(ii) 2.5 Ω connected at port B draws a current of 2 A

For the same network, with 6 V dc connected at port A, 1 Ω connected at port B draws 7/3 A. If 8 V dc is connected to port A, the open circuit voltage at port B is

The impedance looking into nodes 1 and 2 in the given circuit is

A periodic voltage waveform observed on an oscilloscope across a load is shown. A permanent magnet moving coil $$(PMMC)$$ meter connected across the same load reads

An analog voltmeter uses external multiplier settings. With a multiplier setting of $$20\,\,k\Omega ,$$ it reads $$440$$ $$V$$ and with a multiplier setting of $$80$$ $$k\Omega ,$$ it reads $$352$$ $$V.$$ For a multiplier setting of $$40$$ $$k\Omega ,$$ the voltmeter reads

The bridge method commonly used for finding mutual inductance is

For the circuit shown in the figure, the voltage and current expressions are
$$v\left( t \right) = {E_1}\sin \left( {\omega t} \right) + {E_3}\sin \left( {3\omega t} \right)$$ and
$$i\left( t \right) = {{\rm I}_1}\sin \left( {\omega t - {\varphi _1}} \right) + {{\rm I}_3}\sin \left( {3\omega t - {\varphi _3}} \right) + {{\rm I}_5}\sin \left( {5\omega t} \right)$$

The average power measured by the Wattmeter is

A 220 V, 15 kW, 1000 rpm shunt motor with armature resistance of 0.25 Ω , has a rated line current of 68 A and a rated field current of 2.2 A. The change in field flux required to obtain a speed of 1600 rpm while drawing a line current of 52.8 A and a field current of 1.8 A is

A single phase 10 kVA, 50 Hz transformer with 1 kV primary winding draws 0.5 A and 55 W, at rated voltage and frequency, on no load. A second transformer has a core with all its linear dimensions $$\sqrt2$$ times the corresponding dimensions of the first transformer. The core material and lamination thickness are the same in both transformers. The primary windings of both the transformers have the same number of turns. If a rated voltage of 2 kV at 50 Hz is applied to the primary of the second transformer, then the no load current and power, respectively, are

The slip of an induction motor normally does not depend on

The locked rotor current in a 3-phase, star connected 15 kW, 4-pole, 230 V, 50 Hz induction motor at rated conditions is 50 A. Neglecting losses and magnetizing current, the approximate locked rotor line current drawn when the motor is connected to a 236 V, 57 Hz supply is

If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then the region of convergence $$(ROC)$$ of its $$Z$$-transform in the $$Z$$-plane will be

The unilateral Laplace transform of $$f(t)$$ is
$$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$t$$ $$f(t)$$ is

Consider the differential equation
$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$
with $$y\left( t \right)\left| {_{t = 0} = - 2} \right.$$ and $${{dy} \over {dt}}\left| {_{t = 0}} \right. = 0.$$

The numerical value of $${{dy} \over {dt}}\left| {_{t = 0}.} \right.$$ is

If $$x = \sqrt { - 1} ,\,\,$$ then the value of $${X^x}$$ is

Given $$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$ If $$C$$ is a counterclockwise path in the $$z$$-plane such that
$$\left| {z + 1} \right| = 1,$$ the value of $${1 \over {2\,\pi \,j}}\oint\limits_c {f\left( z \right)dz} $$ is

Given that $$A = \left[ {\matrix{ { - 5} & { - 3} \cr 2 & 0 \cr } } \right]$$ and $${\rm I} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],$$ the value of $${A^3}$$ is

The maximum value of $$f\left( x \right) = {x^3} - 9{x^2} + 24x + 5$$ in the interval $$\left[ {1,6} \right]$$ is

The direction of vector $$A$$ is radially outward from the origin, with $$\left| A \right| = K\,{r^n}$$ where $${r^2} = {x^2} + {y^2} + {z^2}$$ and $$K$$ is constant. The value of $$n$$ for which $$\nabla .A = 0\,\,$$ is

Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ The probability that max $$\left[ {X,Y} \right]$$ is less than $$1/2$$ is

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\,\,\,$$ is

A half-controlled single-phase bridge rectifier is supplying an $$R$$-$$L$$ load. It is operated at a firing angle $$α$$ and the load current is continuous. The fraction of cycle that the freewheeling diode conducts is

The typical ratio of latching current to holding current in a $$20$$ $$A$$ thyristor is

In the circuit shown, an ideal switch $$S$$ is operated at $$100$$ $$kHz$$ with a duty ratio of $$50%$$. Given that $$\Delta {i_c}$$ is $$1.6$$ $$A$$ peak-to-peak and $${{\rm I}_0}$$ is $$5 A$$ $$dc,$$ the peak current in $$S$$ is

In the $$3$$-phase inverter circuit shown, the load is balanced and the gating scheme is $${180^ \circ }$$ -conduction mode. All the switching devices are ideal.

If the $$dc$$ bus voltage $${V_d} = 300\,\,V,$$ the power consumed by $$3$$-phase load is

In the $$3$$-phase inverter circuit shown, the load is balanced and the gating scheme is $${180^ \circ }$$ -conduction mode. All the switching devices are ideal.

The $$rms$$ value of load phase voltage is

The bus admittance matrix of a three-bus three-line system is
$$y = j\left[ {\matrix{ { - 13} & {10} & 5 \cr {10} & { - 18} & {10} \cr 5 & {10} & { - 13} \cr } } \right]$$
If each transmission line between the two buses is represented by an equivalent $$\pi \,$$ network, the magnitude of the shunt susceptance of the line connecting bus $$1$$ and $$2$$ is

The sequence components of the fault current are as follows:
$${{\rm I}_{positive}} = j1.5\,pu,\,\,{{\rm I}_{negative}} = - j0.5\,\,pu,$$
$${{\rm I}_{zero}} = - j1\,\,pu.$$ The typeof fault in the system is

For the system shown below, S_D1 and S_D2 are complex power demands at bus $$1$$ and bus $$2$$ respectively. If $$\left| {{V_2}} \right| = 1$$ pu, the VAR rating of the capacitor (Q_G2) connected at bus $$2$$ is

The figure shows a two-generator system supplying a load of $${P_D} = 40\,MW,$$ connected at bus $$2.$$

The fuel cost of generators $${G_1}$$ and $${G_2}$$ are: $${C_1}\left( {{P_{G1}}} \right) = 10,000\,\,Rs/MWhr$$ and $${C_2}\left( {{P_{G2}}} \right) = 12,500\,\,Rs/MWhr$$ and the loss in the line is $$\,{P_{loss(pu)}} = 0.5\,\,P_{G1\left( {pu} \right),}^2\,\,\,\,$$ where the loss coefficient is specified in pu on a $$100$$ $$MVA$$ base. The most economic power generation schedule in $$MW$$ is

A cylindrical rotor generator delivers $$0.5$$ pu power in the steady-state to an infinite bus through a transmission line of reactance $$0.5$$ pu. The generator no-load voltage is $$1.5$$ pu and the infinite bus voltage is $$1$$ pu. The inertia constant of the generator is $$5$$ $$MW-s/MVA$$ and the generator reactance is $$1$$ pu. The critical clearing angle, in degrees, for a three-phase dead short circuit fault at the generator terminal is

The unilateral Laplace transform of f(t) is $$\frac1{s^2\;+\;s\;+\;1}$$. The unilateral Laplace transform of tf(t) is

The input x(t) and output y(t) of a system are related as $$\int_{-\infty}^tx\left(\tau\right)\cos\left(3\tau\right)d\tau$$.The system is

L et y[n] denote the convolution of h[n] and g[n], where $$h\left[n\right]=\left(1/2\right)^nu\left[n\right]$$ and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals

The Fourier transform of a signal h(t) is $$H\left(j\omega\right)=\left(2\cos\omega\right)\left(\sin2\omega\right)/\omega$$. The value of h(0) is