If you have some capacitors in series then their EC (= equivalent capacitance) means the capacitance of the capacitor which will store the same charge as any individual capacitor in the series when the same voltage which is applied b/w first and last plate in the series is applied to it. If the capacitors were in parallel then EC is defined as the capacitance of the capacitor to which for the same voltage as applied to the parallel capacitors then it stores the same total charge.
- But what does EC mean for a general circuit ie circuit consisting of capacitors in series and in parallel?
You may say that it is the capacitance got by simply the circuit by replacing all the capacitors in series and parallel with their equivalent and doing the same until we reduce the circuit either to capacitors in series or parallel, then just use the above definition. Well well well.
-
What if we couldn't reduce the circuit to capacitors in series or parallel? For example, what does EC physically mean for the circuit in this question? Note that I am not asking how to find EC. I am asking for its physical meaning as I gave for capacitors only in series or parallel.
-
A circuit can be reduced to a simple circuit in many ways. How do you prove that for all these ways the EC calculated will be the same?
I have the same question for equivalent resistance.
Best Answer
Stick the capacitor network you want to measure inside a black box. Connect the box in parallel with a DC voltage source with voltage $\Delta V$. Disconnect the box from the source and connect it across a resistor in series with an ammeter. Record the current $I$ through the ammeter as a function of time. Integrate the current to get the total charge $Q = \int dt\, I(t)$ discharged from the capacitor. The equivalent capacitance is $C_{\text{eq}} = |Q / \Delta V|$.