Show that the circuit given in fig. will work as an oscillator at $$f = {1 \over {2\pi RC}},$$ if $${R_1} = 2{R_2}$$

In the circuit of figure $${R_s} = 2\,k\Omega ,$$ $${R_L} = 5\,k\Omega $$ For the op-amp $$A = {10^5},$$
$${R_i} = 100\,k\Omega ,\,\,{R_0} = 50\,k\Omega .$$ For $${V_0} = 10V.$$
Calculate $${V_S}$$ and $${{{V_0}} \over {{V_S}}}$$ and estimate the input resistance of the circuit,

Match the following:
List - $${\rm I}$$ (Circuit)

List - $${\rm II}$$ (Functions)
$$(P)$$$$\,\,\,\,\,$$ High-pass filter
$$(Q)$$$$\,\,\,\,\,$$ Amplifier
$$(R)$$$$\,\,\,\,\,$$ Comparator
$$(S)$$$$\,\,\,\,\,$$ Low-pass filter

One of the applications of current mirror is

A $$NPN$$ Si transistor is meant for low-current audio amplification. Match is following characteristic against their values.

The state-space representation of a system is given by $$\left[ {\matrix{ {\mathop {{X_1}}\limits^ \bullet } \cr {\mathop {{X_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 5} & 1 \cr { - 6} & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right].$$
Find the Laplace transform of the state transistion matrix. Find also the value of $${x_1}$$ at $$t=1$$ if $${x_1}\left( 0 \right) = 1$$ and $${x_2}\left( 0 \right) = 0.$$

The phase lead compensation is used to

The asymptotic magnitude Body plot of a system is given in Figure. Find the transfer function of the system analytically. It is known that the system is minimal phase system.

The number of roots on the equation $$2{s^4} + {s^3} + 3{s^2} + 5s + 7 = 0$$ that lie in the right half of $$S$$ plane is:

None of the poles of a linear control system lie in the right half of $$s$$-plane. For a bounded input, the output of this system

The output of a linear time invariant control system is $$c(t)$$ for a certain input $$r(t).$$ If $$r(t)$$ is modified by passing it through a block whose transfer function is $${e^{ - s}}$$ and then applied to the system, the modified output of the system would be

For block diagram shown in Figure $$C(s)/R(s)$$ is given by

Match the following

In a digital combinational circuit with $$4$$ inputs $$(A, B, C, D),$$ it is required to obtain an output of logical $$1$$ only for the input combination

$$(A = 1; B = C = D = 0).$$ It is known that the following combinations of input are forbidden:

$$ABCD = 1010, 1011, 1100, 1101, 1110, 1111$$
Evaluate the logical expression for the output and realize the same with two input $$NAND$$ gates. Assume that complements of inputs are not available.

The open collector outputs of two$$2$$-inputs $$NAND$$ gates are connected to a common pull up resistor. If the input to the gates are $$P,Q$$ and $$R,S$$ respectively, the output is equal to

In standard $$TTL$$ gates, the totem pole output stage is primarily used to

$$(a)$$ Construct the truth table for the circuit given in Figure $${Q_1},{Q_2}$$ and $${Q_3}$$ are outputs and the clock pulses are the inputs. Unused $$JK$$ inputs are assumed to be at logic $$1.$$ All flip flops are reset at power $$ON$$.
$$(b)$$ Sketch the output waveforms at $${Q_1},{Q_2}$$ and $${Q_3}$$.
$$(c)$$ What function does this circuit perform.

A sinusoidal source of voltage $$V$$ and frequency $$f$$ is connected to a series circuit of variables resistance, $$R$$ and a fixed reactance, $$X.$$ The locus of the tip of the current phasor, $$I$$, as $$R$$ is varied from $$0$$ to $$\infty $$ is

Determine the impedance seen by the source $${V_s} = 24\angle {0^0}$$ in the network shown in Fig.

A circuit consisting of a single resistor $$R$$ and an inductor $$L$$ in series is driven by a $$25$$ $$V$$ $$rms,$$ $$50$$ $$Hz$$ sinusoidal voltage source. A capacitor is to be placed in parallel with the source to improve the power factor. Given that the average power dissipated in the $$R$$ is $$100$$ $$W$$ and that the reactive power delivered to the $$L$$ is $$75$$ $$VAR,$$ what value of $$C$$ will yield a $$0.9$$ $$p.f.$$ lagging as seen by the source?

A circuit with a resistor, inductor and capacitor in series is resonant at $${f_0}\,\,Hz.$$ If all the component values are now doubled, the new resonant frequency is

The switch in the following circuit, shown in Fig. has been connected to the $$12V$$ source for a long time. At $$t=0,$$ the switch is thrown to $$24$$ $$V$$.

$$L = 2\,H,\,\,{R_1} = 10\,\Omega ,\,\,{R_2} = 2\,\Omega ,\,\,C = 0.25\,\mu F$$
$$(a)$$ Determine $${i_L}\left( 0 \right)$$ and $${V_C}\left( 0 \right)$$
$$(b)$$ Write the differential equation governing $${V_C}\left( t \right)$$ for $$t>0$$
$$(c)$$ Compute the steady state value of $${V_C}\left( t \right)$$

Viewed from the terminals $$A, B$$ the following circuit shown in Figure can be reduced to an equivalent circuit of a single voltage source in series with a single resistor with the following parameters:

The effective inductance of the circuit across the terminals $$A,B$$ in the Figure shown below is

In the circuit shown in Figure, it is desired to have a constant direct current $$i(t)$$ through the ideal inductor $$L.$$ The nature of the voltage source $$v(t)$$ must be

A d.c. voltmeter has a sensitivity of $$1000$$$$\Omega /volt.$$ When it measures half full scale in $$100$$ $$V$$ range, the current through the voltmeter is

A moving coil galvanometer is made into a d.c. ammeter by connecting

A symmetrical $$400V,$$ $$3$$-$$\phi $$ supply is connected to the network shown in fig. The phase sequence is $$RYB.$$ Find the reading on the wattmeter

$${R_1} = 30\Omega ,\,\,{X_1} = 50\Omega ,\,\,$$ and $${X_2} = 40\Omega $$

Fig. shows the electrostatic vertical deflection system of $$CRT$$. Given that $${V_A}$$ is the accelerating voltage, the deflection sensitivity (deflection/volt) is proportional to

The figure shows input attenuator of a multimeter. The meter reads full-scale with $$12$$ $$V$$ at $$M$$ with the rage switch at position $$B$$ obtain full-scale deflection with the range switch position at $$D?$$

In a $$50$$ $$KVA,$$ $$11$$ $$KV/400$$ $$V$$ transformers, the iron and copper losses are $$500$$ $$W$$ and $$600$$ $$W$$ respectively under rated conditions. Calculate the efficiency on unity power factor at full load. Find the load for maximum efficiency and the iron and copper losses corresponding to this load.

A $$DC$$ shunt generator delivers $$60$$ $$KW$$ at $$240$$ $$V$$ and $$360$$ $$rpm.$$ The armature and field resistances are $$0.015\,\,\,\Omega $$ and $$60\,\,\,\Omega $$ respectively. Calculate the speed of the machine running as a shunt motor and taking $$60$$ $$KW$$ input at $$240$$ $$V.$$ Allow $$1$$ volt per brush for contact drop.

A synchronous generator connected to an infinite bus is overexcited. Considering only the reactive power, from the point of view of the system, the machine acts as

The armature of a single phase alternator is completely wound with T single turn coils distributed uniformly. The induced voltage in each turn is 2 Volts (rms). The emf of the whole winding is

A 50 Hz transformer having equal hysteresis and eddy current losses at rated excitation is operated at 45 Hz at 90% of its rated voltage. Compared to rated operating point, the core losses under this condition:

A 3-phase squirrel cage induction motor has a full load efficiency of 0.8 and a maximum efficiency of 0.9. It is operated at a slip of 0.6 by applying a reduced voltage. The efficiency of the motor at this operating point is:

The magnetizing current in a transformer is rich in

The efficiency of a 100 kVA transform is 0.98 at full as well as at half load. For this transformer at full load the copper loss.

The laws of electromagnetic induction (Faraday's and Lenz's law) are summarized in the following equation:

Match the following

List-I (Test)
(A) No load and blocked rotor test
(B) Sumpner’s test
(C) Swinburn’s test

List-II (Machine)
(1) Transformer
(2) Induction machine
(3) Synchronous machine
(4) DC machine

A 240 V d.c. shunt motor with an armature resistance of 0.5 $$\Omega$$ has a full load current of 40 A. Find the ratio of the stalling torque to the full load torque when a resistance of 1 $$\Omega$$ is connected in series with the armature?

The laws of electromagnetic induction (Faraday's and Lenz's law) are summarized in the following equation

An electron moves in the $$X$$-$$Y$$ plane with a speed of $${10^6}\,\,m/s.$$ Its velocity vector makes an angle of $${60^ \circ }$$ with $$X$$ axis. A magnetic field of magnitude $${10^{ - 2}}T$$ exists along the $$Y$$ axis. Compute the magnetic force exerted on the electron and its direction.

An infinite number of charges, each equal to $$'q'$$ are placed along the $$x=1,x=2, x=4, x=8, x=16$$ and so on, Find the potential and electric field at point $$x=0,$$ due to these system of charges.

The Laplace transform of $$\,\left( {{t^2} - 2t} \right)\,u\left( {t - 1} \right)$$ is ______________.

The value of $$\,\,\,\int\limits_1^2 {{1 \over x}\,\,\,dx\,\,\,\,} $$ computed using simpson's rule with a step size of $$h=0.25$$ is

If $$A = \left[ {\matrix{ 5 & 0 & 2 \cr 0 & 3 & 0 \cr 2 & 0 & 1 \cr } } \right]$$ then $${A^{ - 1}} = $$

If the vector $$\left[ {\matrix{ 1 \cr 2 \cr { - 1} \cr } } \right]$$ is an eigen vector of $$A = \left[ {\matrix{ { - 2} & 2 & { - 3} \cr 2 & 1 & { - 6} \cr { - 1} & { - 2} & 0 \cr } } \right]$$ then one of the eigen value of $$A$$ is

A set of linear equations is represented by the matrix equations $$Ax=b.$$ The necessary condition for the existence of a solution for this system is

$$A = \left[ {\matrix{ 2 & 0 & 0 & { - 1} \cr 0 & 1 & 0 & 0 \cr 0 & 0 & 3 & 0 \cr { - 1} & 0 & 0 & 4 \cr } } \right].$$ The sum of the eigen values of the matrix $$A$$ is

The uncontrolled electronic switch employed in power electronic converters is

A $$3$$-phsae, fully controlled, converter is feeding power into a $$d.c.$$ load at a constant current of $$150A.$$ The $$r.m.s$$ current through each thyristor of the converter is

When the firing angle $$\alpha $$ of a single phase, fully controlled rectifier feeding constant $$d.c.$$ current into a load is $${30^ \circ }$$ , the displacement power factor of the rectifier is

In a commutation circuit employed to turn off an $$SCR$$, Satisfactory turn-off is obtained when.

The $$MOSFET$$ switch in its on - state may be considered equivalent to

Series capacitive compensation in $$EHV$$ transmission lines is used to

The reflection coefficient for the transmission line shown in figure at $$P$$ is

A shunt reactor of $$100$$ MVAR is operated at $$98$$% of its rated voltage and $$96$$% of its rated frequency. The reactive power absorbed by the reactor is;

A cable has the following characteristics. $$L = 0.201\,\,\mu H/m\,\,$$ and $$\,C = 196.2\,pF/m.\,$$ The velocity of wave propagation through the cable is

Each conductor of a $$33$$ $$kV,$$ $$3$$ phase system is suspended by a string of three similar insulators. The ratio of shunt capacitance to mutual capacitance is $$0.1.$$ Calculate the voltage across each insulator, and the string efficiency.

A power station consists of two synchronous generators A and B of ratings 250 MVA and 500 MVA with inertia constant 1.6 p.u. and 1.0 p.u., respectively on their own base MVA ratings. The equivalent p.u. inertia constant for the system on 100 MVA common base is

An alternator is connected to an infinite bus as shown in figure. It delivers 1.0 p.u. current at 0.8 p.f lagging at V = 1.0 p.u.. The reactance X_d of the alternator is 1.2 p.u. Determine the active power output and the steady state power limit. Keeping the active power fixed, if the excitation is reduced, find the critical excitation corresponding to operation at stability limit.

For the network shown in figure the zero sequence reactances in p.u. are indicated. The zero sequence driving point reactance of the node 3 is

In a power system, the fuel inputs per hour of plants $$1$$ and $$2$$ are given as
$${F_1} = 0.20\,P_1^2 + 30\,{P_1} + 100\,\,$$ Rs per hour
$${F_2} = 0.25\,P_2^2 + 40\,{P_2} + 150\,\,$$

The limits of generators are $$$\eqalign{ & 20 \le {P_1} \le 80\,MW \cr & 40 \le {P_2} \le 200\,MW \cr} $$$
Find the economic operating schedule of generation, If the load demand is $$130$$ $$MW.$$ neglecting transmission losses.

The neutral of $$10$$ $$MVA,$$ $$11$$ $$kV$$ alternator is earthed through a resistance of $$5$$ ohms. The earth fault relay is set to operate at $$0.75$$ $$A.$$ The $$CT's$$ have a ratio of $$1000/5.$$ What percentage of the alternator winding is protected?

Bulk power transmission over long HVDC lines are preferred, on account of

The Laplace transform of $$\left(t^2\;-\;2t\right)u\left(t\;-\;1\right)$$ is