A series circuit consists of an ac source of variable frequency, a 130 resistor,

Question

A series circuit consists of an ac source of variable frequency, a 130 resistor, a 1.00 F capacitor, and a 4.00 mH inductor.

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

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

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

Explanation / Answer

here,

R = 130 ohm

capacitance d, C = 1 * 10^-6 F

inductance , L = 0.004 H

resonance angular frequency , wc = 1/sqrt(L*C)

wc = 1/sqrt(1*10^-6 * 0.004)

wc = 15811 rad/s

A)

when f = fc,

Xl = Xc

then ,

impedance Z = R

impedance = 130 ohm

B)

when w = 2*wc

Z = sqrt( R^2 + ( w*L - 1/w*C))

Z = sqrt( 130^2 + (2* 15811*0.004 - 1/(2*15811*10^-6)))

z = 130.36 ohm

the impedance is 130.36 ohm

C)

when w = wc/2

Z = sqrt( R^2 + ( w*L - 1/w*C))

Z = sqrt( 130^2 + ( 15811*0.004/2 - 1/(0.5*15811*10^-6)))

z = 129.63 ohm

the impedance is 129.63 ohm

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