 #1
annamal
 335
 28
 Homework Statement:
 An RLC series circuit has an impedance of 60 ohms and a power factor of 0.50, with the voltage lagging the current. (a) Should a capacitor or an inductor be placed in series with the elements to raise the power factor of the circuit? (b) What is the value of the reactance across the inductor that will raise the power factor to unity?
 Relevant Equations:

##P = 0.5\times IVcos(\phi)##
##Z = \sqrt{R^2 + (X_l  X_c)^2}##
a) An inductor should be added because that would cancel out the lag of the voltage with the current so that P = IV is at a maximum since V is ahead of I in an inductor
b) ##cos(\phi) = \frac{R}{Z}##, ##R = Zcos(\phi) = 60\times 0.5 = 30 ohms##
##X_l  X_c = \sqrt{Z^2  R^2} = \sqrt{60^2  30^2}## = 52 ohms... don't know how to solve any longer
b) ##cos(\phi) = \frac{R}{Z}##, ##R = Zcos(\phi) = 60\times 0.5 = 30 ohms##
##X_l  X_c = \sqrt{Z^2  R^2} = \sqrt{60^2  30^2}## = 52 ohms... don't know how to solve any longer