# Faraday's Induction and capacitance circuits

Joined Oct 15, 2009
1
Hi all,

Have been given the task of creating a circuit powered by a rotating magnet in a copper coil that will charge a capacitor long enough to light an LED for 600 seconds after the rotating magnet has stopped.

In all the magnet charge up torches I've opened, there are two 3V Lithium Cells (CR 2032) between the generator and the circuit. These cells aren't rechargable though - ? The current from the generator is AC.

I know this shouldn't be too difficult, but can't figure out how to approach it with so many unknown variables. Just looking for any help possible for value of capacitor or resistor.

Voltage for LED = 1.5V
Power for LED ≈ 4mW
Current for LED ≈ 2.7mA
t for capacitance discharge = 600s

EMF = N(dФB)/dt
P = IV
C = Q/V
I = Q/t
F = (A.s)/V

I know that in Faraday's Law of Induction, the magnetic flux in Webers is defined by the equation. But what does the change in time represent? What time is it referring too in the process of passing the magnet through a single loop?

I've entered the values into the capacitance equation and come out with 1.08F. However all capacitors I've found are measured in pF.

Any help at all will be much appreciated.

Thanks

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#### beenthere

Joined Apr 20, 2004
15,819
The capacitor might need to be a "supercapacitor". I have one in my catalog rated 10 Farads @ 5.5 volts as Digi-Key part #283-2806 for \$2.11.

Look up "pseudocapacitor" and you can get up to 220 Farads.

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#### StayatHomeElectronics

Joined Sep 25, 2008
1,020
As far as the capacitors are concerned, look up supercapacitors (supercaps) or ultracapacitors (ultracaps). They commonly come in values of 1F to 10F to 100F and higher. They can get quite expensive at the higher end but the lower end may fit into the range you are looking for.

#### StayatHomeElectronics

Joined Sep 25, 2008
1,020
Let me try a quick explanation.

As you move a coil through a magnetic field, the amount of flux through the coil at any given point in time is different, but theoretically measurable. Therefore, the flux is dependent on, or a function of, time. The equation you have above becomes

$$EMF(t) = N \frac{\delta \Phi_B(t)}{\delta t}$$

The EMF is calculated by considering the change of flux over a given period of time. That is what $$d\Phi$$ and $$dt$$ refer to. It is essentially the slope of the $$\Phi_B(t)$$ curve.

Mathematically, the time increment approaches zero to get the most accurate answer for EMF. The equation becomes $$\frac{d}{dt} \Phi_B$$where differential equations are now used to solve for the EMF. So, the change in time does relate to the coil moving around the magnet but much smaller times are more meaningful.

Here is a reference that you may or may not have seen, but I'll include it for anyone who is interested.