Electric Circuits and Networks

8.13 QUESTIONS

1. Express v(t) = 5 cos(ωt – 45°) – 4 sin(ωt + 30°) as a single complex exponential function.
2. What should be the values of A, ω and φ if the signal v(t) = (2 + j3)e^{j(10t + 0.5π)} + Ae^{j(ωt + φ)} is a real-valued signal?
3. The current in a particular element in a linear circuit excited by a sinusoidal voltage source v_S(t) = 10 cos(100t – 60°) V is found to be i(t) = 0.75 sin(100t –15°) A. (i) What is the complex amplitude of current if v_S(t) = 5e^j200t V? (ii) Explain why you cannot determine the complex amplitude of current when v_S(t) = 5e^j200t V using this data?
4. Express the following signals as phasors by carrying out the addition in the phasor domain. Draw the phasor diagrams.
   1. x(t) = 10 sin500πt + 5 cos(500πt – π/5)
   2. x(t) = 7 sin(120 ...