Consider a circuit consisting of a sinusoidal source vs(t) = cos(t)u(t) volts connected in series to a resistor R and an inductor L and assume that they have been connected for a very long time.
(a) Let R=0 and L=1 H. Compute the instantaneous and the average powers delivered to the inductor.
(b) Let R=1 and L=1H. Compute the instantaneous and the average powers delivered to the resistor and the inductor.
(c) Let R=1? and L=0H. Compute the instantaneous and the average powers delivered to the resistor.
"Hint: In the above parts of the problem use phasors or the trigonometric formula
Cos (a)cos(ß)=0.5[cos(a-ß)+cos(a+ß)]"
(d)The average power used by the resistor is what you pay to the electric company, but there is also are active power for which you do not. The complex power supplied to the circuit is defined as
P =1/2Vs I*
Where Vs and I are the phasors corresponding to the source and the current in the circuit, and I* is the complex conjugate of I. Consider the values of the resistor and the inductor given above, and compute the complex power and relate it to the average power computed in each case.