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

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are there answer choices to this question? this seems like a question where you have options to choose from.