Question

1. Review of phasors. First, if necessary, review the basics of (single-phase) a.c. circuits and phasors in your textbook. Then, answer the following. (a) Making your diagram large enough that you can later add further details, sketch a series circuit consisting of a single loop with • a 115-v.a.c., 60-Hz voltage source, • a 10-kΩ resistor and • a 0.22-µF capacitor in series. (b) Express the voltage source as a phasor [answer: V = (115 v.)e j0 ◦ = 115 v., which you can style with a pencil as V˜ = (115 v.)e j0 ◦ ]. In your diagram. write the voltage source’s phasor characterization next to the voltage source. (c) Compute the complex impedances [resistances] of the capacitor and resistor. For the capacitor, show your work. Write the impedances on the diagram near their respective components. (d) Compute the phasor current I in the loop. Also, add the symbol I with an appropriate directional reference arrow to your diagram. (e) Based on your answer to part d, write a time-domain expression1 for i(t). [Hint: the capacitor enforces a phase shift, so i(t) and v(t), though at the same frequency, will run out of phase with one another.]

Answer 1