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## Homework Statement

Hi, I have virtually no background in electronics and I have been given the following task.

I have to measure the capacitance of the (real) circuit below (using labview, but it is the theory of how to do this that I am interested in).

I am not able to use the obvious method, which is to apply a DC voltage, switch it off and fit the drop in current to an exponential decay function.

**2. The attempt at a solution**

So I have decided to use the relationship C=i/(dv/dt). Apply an alternating voltage and record the current and voltage waveforms, the voltage waveform is then differentiated to give a dv/dt waveform. Then each data point in the current waveform is divided by the corresponding data point in the dv/dt waveform to give the capacitance. (since the division is done element-wise I get a value of capacitance for every point in the waveform/array and just average them to give a more accurate capacitance value, but this is not important)

The problem I have is that the capacitance measurements seem to vary when the input frequency changes, as shown in the graph below.

I think I have also seen a change in the capacitance measurement with changing the amplitude of the input voltage.

**3. Questions - although I would appreciate any ideas on this**

a. Does anyone know why this might happen? - It has been suggested that complex impedance (something which I do not have a good understanding of) is to blame, that there is a phase difference between the current and voltage that needs to be corrected for? - perhaps you could explain this?

b. Can anyone suggest another way to measure the capacitance of this circuit by studying only the current and voltage? (prefereably taking into account of the impedence)

c. Do you think the equation is correct for describing this circuit? - What about the resistor?

d. Can you explain the different sections of the graph? - I think the rise at low frequencies may be due to the capacitor blocking low frequencies and the drop at high frequencies may be due to the capacitor not having enough time to charge when the voltage switches direction....

As I said at the start I have no background in electronics, I have never had a lesson or lecture on it and it was not taught to me at high school, I have really struggled to get to my current understanding of this situation - please don't assume I know what I'm talking about.

Thank you in advance