Power Factor and Resonant Frequency

[eximius]

Homework Statement

[PLAIN]http://img705.imageshack.us/img705/4462/40230468.jpg

Homework Equations

Power Factor = True Power / Apparent Power

f = 1 / (2*pi*root(LC))

Z = root(R^2 + (Xl - Xc)^2) = R

The Attempt at a Solution

a)i) 1? Because it's purely resistive, but this surely can't be right, because it's 4 marks.

ii to iv) no idea

b)i)

f = 1 / (2*pi*root(LC))
f = 64.97 Hz

b)ii) I don't see how the raise in resistance effects the frequency as the resonant frequency formula doesn't contain R.

 

[Zryn]

For part b) i, you are using the a formula that comes about based on some derivations from original principles (resistances in parallel), which works because there is only two reactive elements and no resistance.

For part b) ii, you have a resistance, and thus this formula is not valid for this circuit configuration.

Try to algebraically calculate the equivalent circuit resistance, rationalize the denominator and solve for 'w' based on resonance principles, and you will see where your original formula comes from (when you make R = 0), and you will be able to find the new frequency (now that R != 0).

 

[Zryn]

For part a) i, What do you call a resistance that has magnitude and angle? You are given 3.5$$\angle25$$ in the question.