Section A
Q1.
(a) Let A = \beginbmatrix 5 & -2 & 0 \ -2 & 6 & 2 \ 0 & 2 & 7 \endbmatrix and B = A3 - 2A2 - 5A + 6I, where I is the identity matrix, then calculate the determinant of B.
(b) An infinite number of charges each equal to 'q Coulombs' are placed in a free space along the line at x = 1, x = 2, x = 4, x = 8, x = 16 and so on. Find the expression for potential and electric field intensity at point x = 0, due to these systems of charges. Assume that values of x are in metres.
(c) A Silicon diode that has an ohmic resistance of 0.5 \Omega with reverse saturation current I0 = 10-12A and \eta = 2.0, consumes 50 × 10-12 W extra power compared to ideal diode. Diode operating temperature is 350°K. (i) Determine the fraction of the applied voltage that falls across the ohmic resistance. (ii) Solve part (i), when diode current is 1A. (iii) Compare results of part (i) & (ii) and draw conclusion.
(d) A parallel plate capacitor consisting of two dielectric materials is shown in figure. The middle dielectric slab is placed symmetrically with respect to the plates. If the potential difference between one of the plates and nearest surface of dielectric interface is 4 volts, determine (\epsilon1)/(\epsilon2). Assume parallel plate capacitor has an electrode area of A m2.
