Please answer all parts of the question and show all work. Thank you! An RLC ser

Question

Please answer all parts of the question and show all work. Thank you!

An RLC series circuit has a 2.65 Ohm. resistor, a 115 muH inductor, and a 77.5 muF capacitor. Find the circuit's impedance, m ohms, at 115 Hz. Find the circuit s impedance, in ohms, at 4.5 kHz. If the voltage source supplies an mis voltage of 5.64 V. what is the circuit s mis current, in amperes, at a frequency of 115 Hz? kHz? If the voltage source supplies an mis voltage of 5.64 V. what is the circuit's mis current, in amperes, at a frequency of 4.5 What is the resonant frequency, in kilohertz, of the circuit? What is the mis current. Irms. in amperes, at resonance?

Explanation / Answer

Part a)

We know that in RLC circuit impedance Z = sqrt{R2 +(XL- XC)2}

R =2.65 ohm

XL= 2*pi*f*L = 2*3.14*115*115x10^-6 =0.083 ohm

XC= 1/(2*pi*f*C) = 1/(2*3.14*115*77.5x10^-6) =17.86 ohm

Z = sqrt{2.652 +(0.083- 17.86)2} = 17.97 ohm............Ans.

Part b)

R =2.65 ohm

XL= 2*pi*f*L = 2*3.14*4.5x10^3*115x10^-6 =3.25 ohm

XC= 1/(2*pi*f*C) = 1/(2*3.14*4.5x1000*77.5x10^-6) =0.456 ohm

Z = sqrt{2.652 +(3.25- 0.456)2} = 3.85 ohm............Ans.

Part c)

Current I = V/Z = 5.64 /17.97 =0.313 amp.........Ans.

Part d)

Current I = V/Z = 5.64 /3.85 =1.464 amp.........Ans.

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