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46. | A surface charge density of 8 nc/m^{2} is present on a plane x = z. A line charge density of 30 nC/m is present on line x = 1, y = 2 Find V_{AB} for points A(3, 4, 0) and B(4, 0, 1) |
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Answer: Option A Explanation: Potential due to surface charge ∴ ∴ = 144pv = 452.16v Potential due to line charge at x = 1 and y = 2 |
47. | Which of the following is equivalent to x? |
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Answer: Option B Explanation: Truth table of X-NOR gate :
i.e. when an input to the X-NOR gate is '0' then the other input to the gate is complemented at the output. |
48. | The electric field vector of a wave in free space (ε_{o}, μ_{o}) is |
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Answer: Option C Explanation: Now ∴ _{(use B = μ0 H)} . |
49. | A uniform plane wave is described by the equation H = A/m. If the velocity of the wave is 2 x 10^{8} m/s and ε_{r} = 1.8, then. The frequency of the wave is |
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Answer: Option D Explanation: r = 0.1p . |
50. | Consider two random processes x(t) and y(t) have zero mean, and they are individually stationary. The random process is z(t) = x(t) + y(t). Now when stationary processes are uncorrelated then power spectral density of z(t) is given by |
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Answer: Option C Explanation: The autocorrelation function of z(t) is given by R_{z}(t, u) = E[Z(t)Z(u)] = E[(x(t) + y(t)) (x(u) + y(u))] = E[x(t) x (u)] + E[x(t) y(u)] + E[y(t) x(u)] + E[y(t) y(u)] = R_{x}(E, u) + R_{xy}(t, u) + R_{yx}(t, u) + R_{y}(t, u) Defining t = t - u, we may therefore write R_{z}(t) = R_{x}(t) + R_{xy}(t) + R_{yx}(t) + R_{y}(t). When the random process x(t) and y(t) are also jointly stationary. Accordingly, taking the fourier transform of both sides of equation we get S_{z}(f = S_{x}(f) + S_{xy}(f) + S_{yx}(f) + S_{y}(f) We thus see that the cross spectral densities S_{xy}(f) and S_{yx}(f) represent the spectral components that must be added to the individual power spectral densities of a pair of correlated random processes in order to obtain the power spectral density of their sum. When the stationary process x(t) and y(t) are uncorrelated the cross-sectional densities S_{xy}(f) and S_{yz}(f) are zero ∴ S_{z}(f) = S_{x}(f) + S_{y}(f). |