GATE EE 2014 Question Paper (02-Mar-2014) (Shift 1)

The total power dissipated in the circuit, show in the figure, is 1kW.



The voltmeter, across the load, reads 200 V. The value of X${}_L$ in ohms is __________.

The magnitude of magnetic flux density $\left(\vec{B}\right)$ at a point having normal distance d meters from an infinitely extended wire carrying current of 1 A is $\frac{{\mu }_{0}I}{2nd}$ (in SI units). An infinitely extended wire is laid along the x-axis and is carrying current of 4 A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction μ₀ is permeability of free space Assume $\hat{I},\hat{J},\hat{K}$ to be unit vectors along x, y and z axes respectively.



Assuming right handed coordinate system, magnetic field intensity, at coordinate (2, 1, 0) will be

A discrete system is represented by the difference equation

≤ft[ {*20c X_1≤ft( k + 1 )\\ X_2≤ft( k + 1 ) } ] = ≤ft[ {*20c a&a - 1\\ a + 1&a } ]≤ft[ {*20c X_1≤ft( k )\\ X_2≤ft( k ) } ]

It has initial conditions X₁(0) = 1; X₂(0) = 0. The pole locations of the system for a = 1, are

An input signal $\mathrm{x}(\mathrm{t})=2+5\sin (100\pi \mathrm{t})$ is sampled with a sampling frequency of $400\mathrm{Hz}$ and applied to the system whose transfer function is represented by

$\frac{\mathrm{Y}\left(\mathrm{z}\right)}{\mathrm{X}\left(\mathrm{z}\right)}=\frac{1}{\mathrm{N}}\left(\frac{1-{\mathrm{z}}^{-\mathrm{N}}}{1-{\mathrm{z}}^{-1}}\right)$

where, $\mathrm{N}$ represents the number of samples per cycle. The output $\mathrm{y}[\mathrm{n}]$ of the system under steady state is

A 10 kHz even-symmetric square wave is passed through a bandpass filter the centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output is