GATE EE



The Transconductance of the $$MOSFET$$ is


The voltage gain of the amplifier is





$$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \right)u\left( t \right)$$ with the initial condition $$X\left( 0 \right) = {\left[ { - 1\,\,3} \right]^T}$$ and the unit step input $$u(t)$$ has
The state transition equation
$$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \right)u\left( t \right)$$ with the initial condition $$X\left( 0 \right) = {\left[ { - 1\,\,3} \right]^T}$$ and the unit step input $$u(t)$$ has
The state transition matrix











For the value of $$R$$ obtained in the above question, the time taken for $$95\% $$ of the stored energy to be dissipated is close to

If, at $$t = {0^ + }$$, the voltage across the coil is $$120$$ $$V,$$ the value of resistance $$R$$ is





The power angle is close to
The induced $$emf$$ is close to (line to line)

Assertion [a]: Under V/f control of induction motor, the maximum value of the developed torque remains constant over a wide range of speed in the subsynchronous region.
Reason [r]: The magnetic flux is maintained almost constant at the rated value by keeping the ratio V/f constant over the considered speed range.
(i) at half the rated speed by armature voltage control and
(ii) at 1.5 times the rated speed by field control, the respective output powers delivered by the motor are approximately
Group-I(Performance variables)
(P) Armature emf (E)
(Q) Developed torque (T)
(R) Developed power (P)
Group-II(Proportional to)
1.Flux ($$\phi$$), speed ($$\omega$$) and armature current ($$I_a$$)
2.$$\phi$$ and $$\omega$$ only
3.$$\phi$$ and $$I_a$$ only
4.$$I_a$$ and $$\omega$$ only
5.$$I_a$$ only




Which of the following are valid realizations of the switch $$s$$?


Inertia, M = $$20$$ p.u.; reactance X = $$2$$ p.u. The p.u. values of inertia and reactance on $$100$$ MVA common base, respectively are

The zero sequence driving point reactance at the bus is
The positive sequence driving point reactance at the bus is

$${F_1} = a + b{P_1} + cP_1^2\,Rs/hour$$
$${F_2} = a + b{P_2} + 2cP_2^2\,Rs/hour$$

Where $${P_1}$$ and $${P_2}$$ are the generations in $$MW$$ of $${G_1}$$and $${G_2}$$, respectively. For most economic generation to meet $$300MW$$ of load $${P_1}$$ and $${P_2},$$ respectively, are
