I am trying to understand how to calculate impedance and resonance in a complex RLC circuit.
The circuit (attached) consists of: A 100V RMS AC source, 1.3H inductor, 1k resistor, and a 250pF cap in series, In parallel with the 1.3H inductor and 1k resistor is a 44.2pF cap.
I am trying to calculate and understand how the impedances and resonance work in this circuit.
The calculated Fres is 8,828Hz, but multisim shows the Fres is 8,032Hz (going by Vpk across 250pF cap)
XL=65,606
R1=1K
XC(C1)=448,305
XC(C2)=79,250
It seems to me that the parallel capacitance is shifting the resonance, but I can't seem to get the numbers right. The series capacitance has an XC of 79,250, so I would think at resonance the parallel RLC portion of the circuit should have the same impedance but opposite in phase.
The problem is, the parallel RLC portion of the circuit at 8,032 Hz is capacitive, with a phase angle of -89.85 degrees and a impedance of 56,732 ohms. Here's how I calculated it.
First I took the sum of the XL and R1, then combined it with the XC of C2 using the standard formula for parallel impedances (1/ 1/Z + 1/Z =Zp) = 56,732 ohms.
I calculated the phase angle using: tan^-1((XL-XC)/R) and came up with -89.85 degrees
Can anyone explain what I am doing wrong here?
The circuit (attached) consists of: A 100V RMS AC source, 1.3H inductor, 1k resistor, and a 250pF cap in series, In parallel with the 1.3H inductor and 1k resistor is a 44.2pF cap.
I am trying to calculate and understand how the impedances and resonance work in this circuit.
The calculated Fres is 8,828Hz, but multisim shows the Fres is 8,032Hz (going by Vpk across 250pF cap)
XL=65,606
R1=1K
XC(C1)=448,305
XC(C2)=79,250
It seems to me that the parallel capacitance is shifting the resonance, but I can't seem to get the numbers right. The series capacitance has an XC of 79,250, so I would think at resonance the parallel RLC portion of the circuit should have the same impedance but opposite in phase.
The problem is, the parallel RLC portion of the circuit at 8,032 Hz is capacitive, with a phase angle of -89.85 degrees and a impedance of 56,732 ohms. Here's how I calculated it.
First I took the sum of the XL and R1, then combined it with the XC of C2 using the standard formula for parallel impedances (1/ 1/Z + 1/Z =Zp) = 56,732 ohms.
I calculated the phase angle using: tan^-1((XL-XC)/R) and came up with -89.85 degrees
Can anyone explain what I am doing wrong here?
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