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Trouble with RC Circuit 
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#1
Feb213, 02:59 PM

P: 208

Hello, I'm trying to analyze the RC circuit... specifically a lowpass filter, so the set up is voltage source to resistor to capacitor, and the voltage source provides an oscillating voltage Vin, whereas I measure Vout across the capacitor.
I think I'm getting confused between two different possible analyses: first, comparing Vin and Vout and second, comparing the current and the voltage in the circuit. Please tell me where I'm going wrong. If I consider the ratio Vout/Vin, I have the complex number: 1/(1+iwRC) which has the phase phi1= arctan(wRC). This would imply that at very high w, the output voltage is 90 degrees behind the input voltage. But since at very high w the capacitor drops very little voltage, this circuit is essentially just a resistor dropping all the voltage. So why wouldn't we expect the output and input voltages to be IN phase in this case? Similarly, at very low w the capacitor drops most of the voltage and despite the fact that the phase angle approaches 0 in this limit. Since a purely capacitive circuit has a 90 degree phase shift, shouldn't we expect this shift to be present in that case? I think it would be easier if I could draw a phasor diagram, but I can only draw a phasor diagram to compare Vout (which would be the sum of capacitive voltage and resistive voltage, the two being at right angles to each other) to the current (which is parallel to the resistive voltage)... I wouldn't know where to place Vin on such a diagram would I? Again, I think I'm getting confused between looking at Vout/Vin and Vout/Total current. Please tell me where my errors are! Thank you! 


#2
Feb213, 10:21 PM

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#3
Feb313, 09:47 AM

P: 208

Let's say I draw Vr, the voltage across the resistor, and some angle up from the horizontal axis. Vc, the capacitor's voltage, is 90 degrees behind that. Their sum, which depends on relative lengths, falls somewhere between those two and that would be Vout correct? Where do I draw Vin?



#4
Feb313, 10:11 AM

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Trouble with RC Circuit
Is your problem with where you are putting your voltmeter so that you are apparently getting a phase shift in one case and not in the other?
Relate everything to Earth, to make it easier. If you draw the circuit with the C, connected between Earth and the Resistor and you then connect the source PD to the resistor. The voltage you measure (to Earth) across the capacitor will always be in quadrature with the volts of the supply  just getting less and less as the frequency increases. The phasor diagram can be drawn with Vr along the x axis, Vc along the y axis and Vin will be the diagonal joining those two vectors. Note, I have not used "Vout" because that would either be Vc or Vr, depending on your choice of which one is the 'output' 


#5
Feb313, 11:07 AM

P: 208

Aha! So let me see if I got this right: what I've been calling Vout is really Vc, and Vin is the total of all voltages, what I've called Vtot. So, that's why I've been having the issue with phase shifts if phi is the angle by which current and voltage are out of phase, that's the same as the angle between Vin and Vr (because Vr is in phase with current). But the difference between Vin and Vc (or Vout, as I've used before) is actually 90 degrees MINUS phi, since we're measuring from Vc, and not from Vr, to Vtot?



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