Exercise 3135 A series circuit consists of an ac source of v

Exercise 31.35

A series circuit consists of an ac source of variable frequency, a 105 resistor, a 1.50 F capacitor, and a 5.00 mH inductor.

Part A

Find the impedance of this circuit when the angular frequency of the ac source is adjusted to the resonance angular frequency.

136.10

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Solution

resonance frequency =W = 1/2pi*sqrt(LC) = 1/(2pi*sqrt(5*10^-3*1.5*10^-6)) = 1837.7629 Hz

impedance = R i + (WL - 1/WC) j = 105 i + j(1837.7629*5*10^-3 - 1/(1837.7629*1.5*10^-6) = 105 i -353.57 j

magnitude = sqrt ( 105^2 + -353.57^2) = 368.83 ohm