circuit

1. Graph of a current i(t) A as a function of time t in sec is shown.

1. Find the charge that flows (i) between 0 and 2 sec, and (ii) between1.5 and 6 sec.
2. Assuming the initial charge is 0 C, find the mathematical expression for the charge q(t).
3. Assuming the graph shown is charge q(t) in mC, sketch neatly the graph of current i(t) versus t
4. (a) Express the following set of simultaneous equations in matrix form, [A] [X] = [b]

2x +y-z = 10; 4x-2z = 8; x+3z=-15

(b) Solve the equations to determine the values of x, y, and z.

3. (a) Express the following set of simultaneous equations in matrix form, [A] [X] = [b]

(4-j1) V1 + (3+j1)V2 + (-j10) V3 = 200

(-3-j1) V1 + (6+j4) V2 + (-2-j2) V3 = 0

(-j10) V1 + (4+j2) V3 = 40-j10

(b) Solve the equations for the values of V1, V2, and V3; express them in both rectangular and polar forms. (Express the angle in radians)

4. If V1 = (2+j3); V2 = 1-j1; V3 = 530, compute the values of A = 3V2 – V3, B = V1 V2*, and C = . Express each result in polar form with the angle in degrees..