Answers to problems in Tutorial 1

1. (a) -wLI_0 sin(wt); (b) jwLi(t); (c) -wCV_0 sin(wt); (d) jwCv(t);
2. Voltages at (i) bottom node: 0V; (ii) center node: -2 27/35 V; (iii) bottom right node: 2V; (iv) bottom left node: -4 16/35 V; (v) top right node: -4 37/70 V; (vi) top left node: -2 16/35 V.
3. Current source in series with a voltage source is effectively a current source. Voltages at (i) bottom node: 0V; (ii) center node: -2 9/17 V; (iii) bottom right node: 1V; (iv) bottom left node: -4V; (v) top right node: -4 7/34 V; (vi) top left node: -2V. 1V voltage source is consuming power.
4. Current through the resistor is 1 11/56 A.
5. 6/17 Amps.

Answers to problems in Tutorial 2

1. vo(t) = 10/9 vi(t).
2. (c) 0, approximately 0.111 Volts, 1.111 Volts, -0.111 Volts, -1.111 Volts. (d) There would now be 3 intersection points. vo will now be either +5 Volts or -5 Volts.
3. (a) vo(t) = 2 vi(t); (b) vo(t) = V - vi(t)*RF/R.

Answers to problems in Tutorial 3

1. VTH=3.33V, RTH=5kOhms; Vab=1.25V; max power when RL=5kOhms; 1.1kOhms.
2. -0.15A.
3. VTH=4.62V, RTH=6.31Ohms, R=2.92Ohms.
4. 25.71 Volts.
5. -2/7 Amps.
6. 768W.

Answers to problems in Tutorial 4

1. 60/sqrt(2) angle -120 degrees, or -21.21-j36.74 Volts.
2. 15.3*cos(800*pi*t+56.3 degrees) micro-Amps.
3. 56.5*cos(1000*t+8.07 degrees) Volts.
4. 0.14 - j24.5 Ohms.
5. 0.667*cos(1000t - 80.79 degrees) Amps.
6. IN = 0.1 angle 0 degrees Amps; ZN = 33.7 + j53.9 Ohms.
7. XC = -20 Ohms; 7.96 micro-Farads; XL = 25 Ohms; 3.98 mH.
8. 34.97*cos(120*pi*t-147.5 degrees) Volts.