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Parellel RC with DC voltage source?

This should be a simple analysis. I am analyzing a parallel RC circuit, with a DC voltage source. I have not yet studied AC analysis. The circuit looks like this:

_________ | | | V R C | | | |____|____|

V is really V*u(t), so the voltage is turned on at t=0.

I want to calculate Vc and Vr. On one hand, Vc and Vr should be the same, as they are in parallel. On the other hand, Vc cannot jump to voltage V instantaneously. I have not been able to set up the differential equation to get a solution with any time-varying behavior at the capacitor.

Thanks for any help, especially with setting up the equation to get this right.

Reply to
E. Thomson
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If the R and C are in parallel, the voltage rise across the R and C will be the same. Also, the rise in voltage across the R and C will be entirely dependent on the internal resistance of the DC voltage source and the residual resistance of the wire.

I believe you're thinking about R and C in series. This is covered here:

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Actually, if you can find the internal resistance of your voltage source, you can use this information to calculate the voltage across the R and C for any given time with this information, too.

Good luck Chris

Reply to
CFoley1064

The circuit has only two nodes, so it can have only a single voltage difference between those two points. You have arbitrarily defined the voltage between those two nodes, and it will appear across all paths between those nodes. However, an instantaneous step change in the voltage across the capacitor will require an impulse of current (infinite magnitude, zero duration).

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John Popelish
Reply to
John Popelish

In theory, the charging current is infinite, which differential equations don't like. EE's use the concept of an impulse of current, a pulse of current of zero width but finite charge (the "delta" function, Laplace transform = 1) This is sort of like dividing by zero, and is mathematically iffy.

In real life, there's always some resistance and inductance in the charging path; if you include either or both of these, the circuit becomes mathematically tractable.

John

Reply to
John Larkin

snipped-for-privacy@aol.com (CFoley1064) wrote

entirely >dependent on the internal resistance of the DC voltage source and the residual >resistance of the wire.

OK, so in other words using an ideal source it is correct that there should be no time varying dynamics in the voltage, other than at t=0.

No, that problem is relatively easy to solve, and inspired me to explore other possibilities for theoretical interest. In reality if I build it with a breadboard there is small R in series with V, so the circuit as I've drawn it is mpossible to build. So, basically, I'd get a delta function for current through the capacitor, which would charge up instantaneously, and never discharge.

Thanks. Eric

Reply to
E. Thomson

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