What is the correct voltage current eq. for a variable capacitance capacitor?

In summary, the correct voltage - current equation for a variable capacitance capacitor is: V(t) = C(t)*dv/dt + C(t)*dv/dt.
  • #1
simplex
40
0
What is the correct voltage - current equation for a variable capacitance capacitor?

If the capacitor has a fix value, C, then the following expression holds:

i(t)=C*dv/dt,

where i is the current that charges the capacitor and v the voltage across it.

If C=C(t) then i(t)=C(t)*dv/dt ?!.
Something tells me that this formula is wrong. I am not sure 100% but it looks wrong.


What I need is the correct relation between i(t) and v(t) when C=C(t).
Can I get some help from you?
--------------------------------------------------
Description of the problem in detail:

I have a capacitor whose capacitance, C is a function of time, t. More precisely, the distance between its plates is varied in time, by a mechanical device, according to a known law d=d(t) where d(t) is a function of t only and does not depend of the voltage, current, etc.

As d=d(t) and C=eps*S/d, also C=C(t). So, I can say that I have a capacitor whose capacitance changes in time according to a known, given function, independent of the voltage, current and other electrical parameters and dependent only of the time, t.

This variable capacitor is part of a circuit and as long as I do not know the current - voltage equation of it, I can not go further to analyze the behavior of the circuit which I need for an experiment.
 
Physics news on Phys.org
  • #2
simplex said:
If the capacitor has a fix value, C, then the following expression holds:

i(t)=C*dv/dt,

where i is the current that charges the capacitor and v the voltage across it.

If C=C(t) then i(t)=C(t)*dv/dt ?!.
Something tells me that this formula is wrong. I am not sure 100% but it looks wrong.


What I need is the correct relation between i(t) and v(t) when C=C(t).

The important equation here is:

Q(t) = C(t)V(t)

So,

[tex]I = \frac{dQ(t)}{dt} = V(t)\frac{dC(t)}{dt}+C(t)\frac{dV(t)}{dt}[/tex]
 
  • #3



I understand your concern about finding the correct voltage-current equation for a variable capacitance capacitor. The equation you have provided, i(t)=C(t)*dv/dt, is indeed incorrect. This is because capacitance is not a function of time, but rather a function of the physical characteristics of the capacitor such as the distance between its plates, the type of dielectric material used, etc. Therefore, the correct equation for a variable capacitance capacitor would be:

i(t)=C(t)*dv(t)/dt

Where C(t) is the capacitance at a given time, t, and dv(t)/dt is the rate of change of voltage with respect to time. This equation takes into account the changing capacitance value as the distance between plates changes.

In order to determine the specific equation for your variable capacitance capacitor, you will need to know the function C(t). This can be obtained through experimental measurements or by consulting the manufacturer's specifications. Once you have the function C(t), you can use it in the above equation to calculate the current at any given time.

I hope this helps clarify the correct voltage-current equation for a variable capacitance capacitor. If you need further assistance, I suggest consulting with an expert in the field or conducting further research on the specific type of capacitor you are using. Good luck with your experiment!
 

1. What is the relationship between voltage, current, and capacitance in a variable capacitance capacitor?

The relationship between voltage, current, and capacitance in a variable capacitance capacitor is expressed by the equation Q = CV, where Q is the charge stored in the capacitor, C is the capacitance, and V is the voltage. This means that as the voltage increases, the charge stored in the capacitor also increases, and as the capacitance increases, the charge stored in the capacitor also increases.

2. How does the voltage-current equation for a variable capacitance capacitor differ from that of a fixed capacitance capacitor?

The voltage-current equation for a variable capacitance capacitor is the same as that of a fixed capacitance capacitor, which is Q = CV. The only difference is that in a variable capacitance capacitor, the value of capacitance can change, while in a fixed capacitance capacitor, the value of capacitance remains constant.

3. What factors affect the capacitance of a variable capacitance capacitor?

The capacitance of a variable capacitance capacitor is affected by the surface area of the plates, the distance between the plates, and the type of dielectric material used. Increasing the surface area or decreasing the distance between the plates will increase the capacitance, while using a higher dielectric constant material will also increase the capacitance.

4. Is there a maximum voltage or current that a variable capacitance capacitor can handle?

The maximum voltage and current that a variable capacitance capacitor can handle depends on its design and construction. Generally, variable capacitance capacitors have lower voltage and current ratings compared to fixed capacitance capacitors. It is important to check the datasheet or specifications of the specific capacitor to determine its maximum ratings.

5. How is a variable capacitance capacitor used in practical applications?

Variable capacitance capacitors are commonly used in tuning circuits for radios, televisions, and other electronic devices. They can also be used in filters, oscillators, and other circuits where the capacitance needs to be adjustable. In these applications, the capacitance of the variable capacitor is adjusted to control the frequency or signal strength of the circuit.

Similar threads

Replies
7
Views
1K
  • Electromagnetism
Replies
7
Views
874
Replies
7
Views
1K
  • Electromagnetism
Replies
1
Views
674
Replies
1
Views
1K
Replies
3
Views
938
  • Electromagnetism
Replies
4
Views
855
  • Electromagnetism
Replies
6
Views
996
Replies
17
Views
388
Replies
3
Views
1K
Back
Top