🚀 go-pugleaf

Please help me to invent a water analogy for the capacitors in series.
I have no trouble with an analogy for parallel capacitors (see below). I
suspect that my failure to conceive a valid analogy of capacitors in series
may somehow be related to the "myth of equal charges".

                HYDRAULIC ANALOGY FOR PARALLEL CAPACITORS

                                                     C1         C2
I                                       I         I      I    I    I
I ............  large lake .............I         I......I    I....I
I      acts as a source of constant     I         I      I    I    I
I            level difference           I         I      I    I    I
I.......................................I         I......I    I....I
I.......................................I         I......I    I....I
I.......................................I         I......I    I....I
I                                       -----------      ------    I
I.....................................   long pipe .... short pipe I
-------------------------------------------------------------------I

Suppose that containers C1 and C2 (corresponding to two capacitors) are
connected to a lake with a horizontal pipe at zero level. Containers are
initially empty (the valve in the long pipe is closed). At time t=0 the
valve is open and water starts flowing through the long pipe filling the
containers. The rate of flow, at any given time, is proportional to the
level difference between the lake and containers (I assume that the pipe
between C1 and C2 is short and thick so that levels in C1 and C2 are
essentially identical). This observation can be written in the form of a
differential equation whose solution is the exponential decrease of water
current. For large t the current is zero and the level in C1,C2 is the same
as in the lake. But the amounts of water in the containers, Q1 and Q2, are
different. In this analogy volumes are "mechanical capacitances".

BUT HOW CAN A HYDRAULIC SYSTEM BE INVENTED IN WHICH CONTAINERS ARE AT TWO
DIFFERENT LEVELS (TO MAKE V1+V2=V=LAKE)? THAT SYSTEM MUST BRING WATER
TO C1 VIA C2, OR VICE VERSA, AND ITS FINAL EQUILIBRATED STATE SHOULD BE
Q1=Q2 (EVEN WHEN VOLUMES OF C1 AND C2 ARE DIFFERENT).

I do not think that mechanical analogies must exist for all nonmechanical
systems. But in this case the failure to conceive an analogy (if confirmed)
may be used as an ADDITIONAL argument that "equilibrated charges on capacitors
in series are not equal". How appealing is this argument? Will it help to
convince textbook writers that something is wrong with the electrostatic
model for equilibrated charges?

                 Ludwik Kowalski    kowalski@apollo.montclair.edu