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## Tuesday, September 27, 2005

### RC circuit analogy

For the EE's out there, I figured out a neat trick to cast the continuous oil shock model into a simple electrical RC (resistive/capacitive) circuit, with Kirchoff's law describing the differential equation.

I(t) = C * dV(t)/dt + V(t)/R(t)
I(t) acts as the forcing function (the black circle with the arrow pointing up), a source of current representing the tapped reserves. If you think of electrons as equivalent to oil molecules, then electron current becomes the amount of oil filling up our reserve capacity per unit of time and voltage V(t) represents cumulative charge of oil, more or less. Note how the capacity, low and behold, turns into the the capacitance C of the circuit. If the forcing function gets turned off (note the switch), then the amount drained off as oil production becomes the V(t)/R(t) term. Actually, 1/R(t) represents the reciprocal of resistance, i.e. conductance, of the circuit, which indicates the proportional amount bled from the reservoir capacity. The arrow through the resistor symbol makes it variable, as in a potentiometer.

Get yourself a good programmable current source with a storage oscilloscope measuring the shunted current through the resistor, and you can make your own Analog Peak Oil Simulation!1

TOD posted notes from Rep. Bartlett's recent Energy Conference. This quote concerning Heinberg got me thinking:
He thinks Katrina and Rita have catapulted us into a bumpy plateau instead of a clear peak.
What does this mean? Somebody will have to turn the potentiometer up to 11 very soon!

1Or you can run the circuit through a Spice simulator, or you can try solving the equations using Laplace transformations, or ?