Question

A series circuit consists of an ac source of variable frequency, a 110 ? resistor, a 1.20 ?F capacitor, and a 4.10 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.

Answer 1

here,

resistance ,R = 110 ohm

capacitance , C = 1.2 uF = 1.2 * 10^-6 F

inductance ,L = 4.1 mH = 0.0041 H

the resonance frequency , w = 1/sqrt(L*C)

w = 1/sqrt(0.0041 * 1.2 * 10^-6) rad/s

w = 1.4 * 10^4 rad/s

a)

the impedance of this circuit when the angular frequency of the ac source is adjusted to the resonance angular frequency , Z = sqrt(R^2 + (w * L - 1/(w*C))^2)

Z = sqrt(110^2 + ( 1.4 * 10^4 * 0.0041 - 1/( 1.4 * 10^4 * 1.2 * 10^-6) )^2) ohm

Z = 110 ohm

b)

the impedance of this circuit when the angular frequency of the ac source is adjusted to twice the resonance angular frequency , Z = sqrt(R^2 + (2*w * L - 1/(2*w*C))^2)

Z = sqrt(110^2 + ( 2.8 * 10^4 * 0.0041 - 1/( 2.8 * 10^4 * 1.2 * 10^-6) )^2) ohm

Z = 139 ohm

c)

the impedance of this circuit when the angular frequency of the ac source is adjusted to half the resonance angular frequency , Z = sqrt(R^2 + (0.5*w * L - 1/(0.5*w*C))^2)

Z = sqrt(110^2 + ( 0.5 * 1.4 * 10^4 * 0.0041 - 1/( 0.5 * 1.4 * 10^4 * 1.2 * 10^-6) )^2) ohm

Z = 142.3 ohm