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Experiment to show that current leads voltage by 90 degrees in capacitor

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Edward Yuen

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Many books told us current leads voltage by 90 degrees in capacitor. I know why it is 90 degrees.
But, how to show that it is true by an experiment?
 

Put a small sense resistor in series between
cap and ground, drive the other end of the cap
with a sine wave, put both the drive signal and
sensed-current voltage on the 'scope, there it
is. For even more accuracy you could display
the difference voltage acoss the cap, if your
'scope has math functions.
 

I rather would say that "voltage lags current by 90 deg".
Why? Because such a "leader function" is physically not possible.

More than that - would you connect a voltage source to a capacitor to see how the current behaves?
No - of course not.
We try to inject a sinusoidal current into the capacitor (using a voltage source and a suitable series resistor) and measure the phase shift between the current into and the volage across the capacitor.
 

Many books told us current leads voltage by 90 degrees in capacitor. I know why it is 90 degrees.
But, how to show that it is true by an experiment?

Number 1: voltage is the causative factor; it is the application of a potential that causes the current. The current is determined by Ohm's law. If you consider the instantaneous charge on the capacitor as a voltage source, then Ohm's law applies at every point.

Number 2: This experiment is impossible to perform in real life; this is a steady state approximation. Consider you apply an ideal voltage source of 1v and 100Hz frequency to an ideal capacitor; the current will be infinite (unless you apply the voltage at the zero crossing moment)in the beginning. However, in real life the voltage sources have finite impedance and the capacitors are far from ideal.

Number 3: You use an RC circuit (so that you avoid the infinite current problem) and measure the voltage across the R and C using electrometer probes. Assume that the voltage across the resistor is proportional to the current (true for ideal resistors) and you can see that the phase of the current and voltage on an oscilloscope. The finite value of R will make the phase difference not exactly equal to 90 deg
 
Hi,

In my eyes it should be a demonstration to view the behaviour.
I may be mistaken, but I don't think this experiment is about absolute exactness, it doesn't whether voltage causes current or vice versa....

If so, then you need a capacitor for AC, the bigger the better....something to measure the current...and something to visualize both.
The first that comes into my mind is an oscilloscope...with a small resistor for the current measurement.
And yes, it will not be exactly 90°.

Klaus
 

If you are teaching a bunch of students (that I have done in my previous life), then I suggest that you also explain the principle of charge storage before everything. Perhaps you may begin at the beginning- with a Leyden jar!

Then also take some time to explain the charge and potential relation for a capacitor. The concept is important because every electronic component has some capacitance associated with it.

The consider the sine wave and explain step wise. Starting from zero, the voltage in the beginning is increasing rapidly and so the capacitor is also charging up rapidly. Now the capacitor is looking like a voltage source that is in opposition to the applied voltage. So in each step the current will be determined by the increase in the voltage (current voltage, this is the applied voltage at this moment - minus the charge on the capacitor which is equal to the voltage in the previous step). So, for the capacitor the current is proportional to the rate of increase of the potential. The rate of increase in potential is zero at the peak and hence the current is zero when the voltage is at the peak. This shall explain why the phase shift should be 90 between the the current and voltage waveform. At each step current is infinity (and hence cannot be measured) but is proportional to the increase in the voltage (rate change).

After this notional explanation, you can setup some experiment to demonstrate the phenomenon experimentally.
 

Some comments.

Ohms law has been derived for DC circuits. Although you can apply similar relations to AC circuits and AC impedances, I think it's misleading to talk about Ohms law in this context.

The discussion if capacitor voltage is determined by a current or in reverse current determined by a voltage is in my opinion just useless. You can create experimental setups for both dependencies. Similarly I can't share the preservations against "leader function" expressed in post #3. Leading current isn't about causality, just a describing phase relation of sinusoidal voltage and current.

If I should setup the experiment, I would use
- isolated voltage source (a low voltage safety transformer)
- R and C (kOhm and µF range)
- two channel oscillosope with single ended probes or simply banana jack adapters
 
If I should setup the experiment, I would use
- isolated voltage source (a low voltage safety transformer)
- R and C (kOhm and µF range)
- two channel oscillosope with single ended probes or simply banana jack adapters
It would be interesting to see a simulation of an applied voltage of 10V amplitude, 50Hz freq, 1 K resistor and 1uF capacitor.

I doubt you will ever get a 90deg phase shift.
 
Thanks for your replies!
I have designed a simple experiment to show that it is true within the experimental errors and wanted to know whether there is another method to show that it is true. (One of the experimental errors arises from the accuracy of my scope. )
--- Updated ---

I used a series RC circuit. R is 22k ohm. C is 0.01 micro farad. Source is 4Vpp with 500Hz/1000Hz/1500Hz Sine Wave.
My scope will jump from 148 micro second to 152 micro second (instead of 149 micro second) when I measured the phase difference using
cursor of scope. So, there is experimental error due to my accuracy of my scope.

My experimental result: 89.28 ° (500Hz)
90.72 ° (1000Hz)
89.46 ° (1500Hz)

Besides, I used 1.2 k ohm, 1 micro farad capacitor and 100 Hz Sine Wave. The result is 89.28 °
 
Last edited:

    c_mitra

    Points: 2
    Helpful Answer Positive Rating
I used the phasor diagram of RC circuit to analyse the experiment. If the angle between Vr and Vs is θ and
the angle between Vs and Vc is Φ . The addition of θ and Φ should be near to 90 °
( Vr : voltage of resistor;
Vs : voltage of source;
Vc : voltage of capacitor;
I : current )

Then, I found the angles of θ and Φ in the experiment.

Since Vr and I are in the same phase and the addition of θ and Φ is near to 90 ° ,
I showed that the current leads voltage by 90 ° in capacitor.
 

Error terms to be considered are capacitor loss factor and probe impedance in parallel to the capacitor. For example, tan \( \delta \) of 0.01 (X/R = 0.01) corresponds to an error of 0.57 degree. Respectively measured phase angle would be 89.4 degree Acceptable for a principle experiment, I think. As reported by the original poster, oscilloscope measurement accuracy is additionally affecting the results.
 
If the accuracy of scope of somebody is better than the accuracy of my scope.
For example, if each jump of the cursor of scope is 1µ s ( Δ x/ Δ t), the angle would be 89.99 ° or 90 ° .
(Each jump of my scope is 4µ s)

Besides, my method to find θ and Φ is
(1) using high pass RC circuit to find θ
(2) then, using low pass RC circuit to find Φ (exchange the positions of resistor and capacitor in the circuit).

On the other hand, we need not exchange the positions of resistor and capacitor
but move the source, the ground lead , the probes of CH1 and CH2 to other positions of the circuit.
We can also find Φ.
 
Last edited:

I'd prefer a circuit that directly visualizes the 90 degree phase shift, like below

1597678774925.png
 
I have a video in youtube about the experiment :
Experiment 1: Show that current leads voltage by 90 degrees in capacitor (Using Oscilloscope)

where the phase difference between Vr and Vs and the phase difference between Vs and Vc are seen on scope.
 

Experiment 1: Show that current leads voltage by 90 degrees in capacitor (Using Oscilloscope)

 
Last edited:

Many books told us current leads voltage by 90 degrees in capacitor. I know why it is 90 degrees.
But, how to show that it is true by an experiment?
voltage is the causative factor; it is the application of a potential that causes the current. The current is determined by Ohm's law. If you consider the instantaneous charge on the capacitor as a voltage source, then Ohm's law applies at every point.
 

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