Re: Can anyone solve this problem?

["Carl E. Mungan" <mungan@USNA.EDU>]

> In the arrangement shown in the figure, a potential difference V
> is applied, and C1 is adjusted so that the voltmeter between
> points b and d reads zero.  This "balance" occurs when C1 = 4.00
> microF.  If C3 = 9.00 microF and C4 = 12.0 microF, calculate the
> value of C2.
>
>         ______________________
>        |         |            |
>        | V      ===C1  ___   ===C4
>      -----      b|____/ V \___|d
>       ---        |    \___/   |
>        |        ===C2        ===C3
>        |_________|____________|

Hmm... that reminds me of my old question about how we know that the
charges on capacitors in series are equal:
http://physics.usna.edu/physics/faculty/mungan/capacitors.html

In fact, if I didn't know how to solve the Wheatstone resistor bridge
problem where the capacitors are replaced by resistors in the circuit
above, I am vanishingly close to 100% certain I could not solve the
problem John has posed above. The difference is in the resistor
problem I can think about the fact that there can't be any net
current through the meter after everything has settled down and hence
the current through 1 and 2 must be equal.

But in the above problem, it is not at all obvious that there
couldn't have been charge flow through the meter *while* things are
settling down, so that the charges on 1 and 2 need not be equal.

To me, the lesson is: Solve problems by doing analogies with problems
you already know how to solve. Compare them, find ways they are
similar, and use this to decide how to tackle (or in this case,
finesse away) the differences.
--
Dr. Carl E. Mungan, Asst. Prof. of Physics   410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Annapolis, MD 21402-5026     mailto:mungan@usna.edu
            http://physics.usna.edu/physics/faculty/mungan/