Re: How to set up a diff equation for circuit with a diode?

• To: mathgroup at smc.vnet.net
• Subject: [mg62809] Re: How to set up a diff equation for circuit with a diode?
• From: dh <dh at metrohm.ch>
• Date: Mon, 5 Dec 2005 13:41:31 -0500 (EST)
• References: <dn0v2m\$8g2\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,
your question mnust be rephrased. The diode either has no effect or
blocks all current.
If the diode has no effect, the initial current of I0 changes with time
exponentially to V/R. For this case we have (I call the current C
because I already has a meaning):
L C'[t]  + R C[t] -V == 0

the analytic solution to this is (in its full glory):
\!\(\(\[ExponentialE]\^\(-\(\(R\ t\)\/L\)\)\ \((C0\ R + \((\(-1\) + \
\[ExponentialE]\^\(\(R\ t\)\/L\))\)\ V)\)\)\/R\)

Using NDSolve, you will first have to give numerical values to the
constants and then you would write:

rep = {R -> 1, L -> 1, V -> 1, C0 -> 2};
NDSolve[{L C'[t] + R C[t] - V == 0, C[0] == C0} /. rep, C, {t, 0, 2}]

this gives an InterpolatingFunction that can be plottedt e.g. by:

Plot[(C /. res[[1]])[t], {t, 0, 2}]

Daniel

siliconmike wrote:
> I'm kind of curious how to set up a nonlinear differential equation and
> then solve it using NDSolve in case of the following setup:
>
> Battery V in series with a diode, R and L.
>
> To simplify, we may assume that diode is a pure conducting device in
> forward direction and pure blocking device in the reverse direction.
>
> Now how to set up a differential equation for the current I(t), that is
> solvable using NDSolve?
>
> Thanks
> Mike
>

```

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