A 402-Ohm resistor, an inductor, and a capacitor are in series with an AC source

Question

A 402-Ohm resistor, an inductor, and a capacitor are in series with an AC source. The reactance of the inductor is 697 ohm, and the circuit impedance is 767 Ohm. (a) What are the possible values of the reactance of the capacitor? (b) If you find that the power delivered to the circuit decreases as you raise the frequency, what is the capacitive reactance in the original circuit? (c) Repeat part (a) assuming the resistance is 201 Ohm instead of 402 Ohm and the circuit impedance continues to be 767 Ohm.

Explanation / Answer

resistance R=402 ohms

reactance of inductor, XL=697 ohms

impedance Z=767 ohms

reactance of capacitor is Xc

a)

impedance Z=sqrt(R^2+(Xc-XL)^2)

767=sqrt(402^2+(Xc-697)^2)

==> Xc=43.9 ohms or Xc=1350.2 ohms

b)

XC=43.9 ohms

c)

impedance Z=sqrt(R^2+(Xc-XL)^2)

767=sqrt(201^2+(Xc-697)^2)

==> Xc=1437.2 ohms or Xc=43.2 ohms

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