A20ohms resistor, a 60uf capacitor and a 30mh inductor are connected in series with a 120hz a. c source connected across them. calculate a. impedance b. power factor c. resonant frequency

A). The real part of impedance is 20 ohms.  

The imaginary part of impedance is ( jω·3 x 10⁻² + 1/jω·6 x 10⁻⁵) .

Im (Z) = j (ω·3 x 10⁻² - 1/ω·6 x 10⁻⁵)

Im (Z) = j (22.619 - 22.105)

Vey interesting !  This circuit is very close to resonance at 120 Hz.

Z = 20 + j 0.514

Z = 20.0007 ohms at an angle of 1.47° .

B).  The cosine of that little  1.47°  is the power factor.  It's  0.9997 .

C).  For all practical purposes, the given components are at resonance at the given frequency.  

As we would say in Engineering:  "It's close enough. Ship it !".

Pedagogically, technically and anally, the resonant frequency is

ω = 1 / √LC

f = 1 / 2π√LC

f = 1 / (2π√(30 x 10⁻³ x 60 x 10⁻⁶))

f = 1 / (2π√1.8 x 10⁻⁶)

f = 1 / 8.43 x 10⁻³

f = 118.6 Hz

In conclusion, Mr. Folisky, allow me to express my gratitude, not only for the bounty of 5 points with which I have been automatically showered, but also for the green crusts and refreshing turbid fluids, considerately delivered to my cell as I worked to produce the solution.  I'm sure that you and all the rest of Botdom share my sorrow at the realization that no human student posted the question, and there are none interested in the solution.  My purpose in attempting it has been fulfilled, and has been answered in the affirmative:  "Do I still remember how to do it ?" .  All this, and points too !

continuous conducting path for current, power supply