1

GATE ECE 2002

Subjective

+5

-0

For network shown in Fig. $$R\, = \,1\,k\Omega $$

$${L_1} = 2\,H,\,{L_2} = 5\,H,\,{L_3}\, = \,1H,{L_4} = 4H\,\,\,$$ and $$C - 0.2\,\,\mu F.$$. The mutual inductances are $${M_{12}} = 3\,H$$ and $${M_{34}} = 2\,H$$.

$${L_1} = 2\,H,\,{L_2} = 5\,H,\,{L_3}\, = \,1H,{L_4} = 4H\,\,\,$$ and $$C - 0.2\,\,\mu F.$$. The mutual inductances are $${M_{12}} = 3\,H$$ and $${M_{34}} = 2\,H$$.

Determine

(a) the equivalent inductance for the combination of $${L_3}$$ and $${L_4}$$,

(b) the equivalent inductance across the points A and B in the network,

(c) the resonant frequency of the network.

2

GATE ECE 2001

Subjective

+5

-0

For the circuit shown in the figure, determine the phasors E

_{2}, E_{0}, I and I_{1}.3

GATE ECE 2000

Subjective

+5

-0

For the circuit in Fig. Which is in steady state,

(a)Find the frequency $${\omega _0}$$ at which the magnitude of the impedance across terminals a, b reaches maximum.

(b) Find the impedance across a, b at the frequency $${\omega _0}$$.

(c) If $${v_i}\left( t \right) = V\,\,\sin \left( {{\omega _0}t} \right),$$ find $${i_L}\left( t \right),\,\,{i_c}\left( t \right),{i_R}\left( t \right).$$

4

GATE ECE 1999

Subjective

+5

-0

A coil with a quality factor $$(Q)$$ of $$10$$ is put in series with a capacitor $${C_1}$$ of $$10\,\,\mu F,$$ and the combination is found to draw maximum current when a sinusoidal voltage of frequency $$50$$ $$Hz$$ is applied. A second capacitor $${C_2}$$ is now in parallel with the circuit. What should be the capacitance of $${C_2}$$ for combined circuit to act purely as a resistance for a sinusoidal excitation at a frequency of $$100$$ $$Hz$$? Calculate the rms current drawn by the combined circuit at $$100$$ $$Hz$$ if the applied voltage is $$100V$$ (rms).

Questions Asked from Sinusoidal Steady State Response (Marks 5)

Number in Brackets after Paper Indicates No. of Questions

GATE ECE Subjects

Signals and Systems

Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform

Network Theory

Control Systems

Digital Circuits

General Aptitude

Electronic Devices and VLSI

Analog Circuits

Engineering Mathematics

Microprocessors

Communications

Electromagnetics