# Is the capacity of a capacitor in an RC circuit independent of time? If so why?

Is the capacity c of a capacitor independent of time in an RC circuit?

In the notes through which I'm working the following step is made:

$$\frac{d}{dt}Q=\frac{d}{dt}(uc)=c\frac{d}{dt}u$$

the final equality is implies that c is independent of time but why? (I have a very elementary background in circuits...)

• Capacity is not capacitance. Capacity more or less relates to how much voltage a capacitor can tolerate before breaking down. Commented Apr 21, 2020 at 16:29

If your ideal circuit uses an ideal capacitor then yes, that capacitance will be constant. This is simply by our definition of the ideal capacitor element.

Having said that, there are situations in real circuits where the capacitance can change as a function of time or of applied voltage.

Basically, for a simple capacitor Q (charge) = capacitance x voltage. So, if there was a voltage across two plates of a capacitor, charge (Q) would be C.V and, if you halved the distance between those plates by bringing them closer AND, with no further introduction of new charge or energy, capacitance would double and the voltage would naturally halve to ensure that charge is conserved.

Thus Q = CV is maintained.

If you then remembered that the rate of change of Q is current (i) then you could say this: -

$$i = C\dfrac{dV}{dt}$$

But equally, you could say this: -

$$i = V\dfrac{dC}{dt}$$

Or you could construct whatever mathematical relationship that satisfied the basic charge equation, whether you alter voltage or alter capacitance or a mixture of both.

ceramic capacitors, particularly the very compact and cheap varieties, will use mixes of ceramic that VARY A LOT with the voltage---- even 50% or 80%.

You don't want to use these high dC/dV capacitors in MUSIC circuits.

If it's an electrolytic capacitor, its capacity is a function of time and operating temperature ... on a scale of years or decades it may lose most of its capacity.

But otherwise? ... no.

The capacitance of a capacitor, its voltage rating, and its frequency characteristics are determined by the kinds of materials used and their physical arrangement. Note that the total energy stored in a capacitor is dependent on both the capacitance and the terminal voltage. A 1 uF capacitor charged up to 10 V stores four times the energy of the same capacitor charged up to only 5 V.