Here's a thought experiment with some maths, inspired by reading some old Tesla patents.
Take one 1uF, 25V capacitor and build a circuit powered by a 12V battery. Assume 1 ohm resistance.
After 5 time constants the charge on the capacitor will be 99.3% of 12V, which is 11.916V.
One time constant is:
t = RC
t = 1 x 0.000001
t = 0.000001 seconds
5t = 0.000005 seconds = 5 microseconds
Therefore the capacitor will be charged to 11.916V after 5 microseconds.
The energy stored in a capacitor is:
E = (CV
2) / 2
E = (0.000001 x 11.916
2) / 2
E = 0.000070995528 J
There are 1,000,000 microseconds in a second, so we would be able to charge & discharge the capacitor 200,000 times per second.
Assuming we discharge the capacitor and recharge it cyclicly, making use of the stored energy, then after 1 second we would have accumulated:
200,000 Hz x 0.000070995528 J =
14.1991056 Watts (1 J per second is 1 Watt)
Now, consider that voltage is essentially free. It's relatively easy to generate extremely high voltages with extremely low currents.
If instead of 12V our circuit operated at 20,000V and our capacitor was rated at 20kV, then the calculation would look like this:
99.3% of 20kV = 19,860V
E = (CV
2) / 2
E = (0.000001 x 19,860
2) / 2
E = 197.2098 J
200,000 Hz x 197.2098 J = 39,441,960 Watts =
39.44196 MegawattsIf our circuit operated at 40,000V then the calculation would look like this:
99.3% of 40kV = 39,720V
E = (CV
2) / 2
E = (0.000001 x 39,720
2) / 2
E = 788.8392 J
200,000 Hz x 788.8392 J = 157,767,840 Watts =
157.767840 MegawattsHere are some examples that I put together in the Falstad circuit simulator:
https://tinyurl.com/23y9wzcj
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Topic: If you knew how simple it was you would laugh (Read 8517 times)
