Electronics and Communication Engineering - Exam Questions Papers

Consider

Number of samples per period = 10p

This is not a rational number. Hence signal is non periodic.

The area of the shaded region

.

Statement 1 is false, since f{h(t)e^3t} corresponds to the value of the Laplace transform of h(t) at s = 3.

If this converges, it implies that s = - 3 is in the ROC.

A casual and stable system must always have its ROC to the right of all its poles. However, s = - 3 is not to the right of the pole at s = - 2.

Statement 2 is false, because it is equivalent to stating that H(0) = 0. This contradicts the fact that H(s) does not have a zero at the origin.

Statement 3 is false. If h(t) is of finite duration, then if its Laplace transform has any points in its ROC, ROC must be the entire s-plane.

However, this is not consistent with H(s) having a pole at s = - 2.

Statement 4 is false. If it were true, then H(s) has a pole at s = - 2, it must also have a pole at s = 2.

This is inconsistent with the fact that all the poles of a causal and stable system must be in the left half of the s-plane.

A quantity of any substance equal to its molecular weight in grams is a mole of that substance contains the same number of molecules as one mole of any other substance. This Avogadro's number and equals 6.02 x 10²³ molecules per mole. Thus

= 9.03 x 10²⁸ electrons/m³

Since for tungsten the atomic and the molecular weights are the same. Therefore for tungsten

E_F = 3.64 x 10^-19(η)^2/3

= 3.64 x 10^{- 19}(9.03 x 10²⁸)^2/3

E_F = 7.326 eV.

∴ V_P = 3.46 x 10⁸ m/s.