a circuit exhibiting exponential decay ??

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wdflannery
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a circuit exhibiting exponential decay ??

Post by wdflannery » Fri Jun 10, 2005 12:07 pm

The idea is to wire up an easy circuit to demonstrate an exponential function. So, I started with a 1 f double layer electric capacitor, a 1.5 volt battery, and a flashlight lamp in series. The circuit should have had a time constant of > 1 sec, yet nothing happened. I think I don't understand double electric layer caps. What is their internal resistance? Should this circuit work?<p>How about a 0.1 f electorlytic in series with a LED, a 10 ohm resistor, and a battery? What's the internal resistance for a 0.1 f electrolytic.<p>Or, put the cap and LED or lamp + resistor in parallel, charge up the cap, and disconnect the battery letting the cap discharge through the LED and resistor? How does the LED affect the circuit?<p>
The circuit needs to be really simple as above and should ideally show a slow exponential decay.

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Chris Smith
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Re: a circuit exhibiting exponential decay ??

Post by Chris Smith » Fri Jun 10, 2005 1:28 pm

You bled off the cap too fast. <p>Flash Light bulbs usually draw a half amp or so, and your cap has the current stored up to about 1/10th or less of that, per second, hence the 1/10th of a second charge and delay while draining. <p>What you need is a resistor in line so the formulae R/C applies, and decays in accordance with the whole Formulae. <p>But the voltage drops also, and so a led and Resistor would be better. Smaller current draw, and its still bright.

If you attach a led straight with no resistor, it will do the same and probably blow the led for drawing too much too fast which is why current resistors are used on leds in the first place.

pebe
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Re: a circuit exhibiting exponential decay ??

Post by pebe » Fri Jun 10, 2005 3:42 pm

Assuming your 'f' is intended to mean Farads, then your circuit should have worked. The lamp probably draws about 200mA at 1.5v, so its resistance would be around 7.5ohms (it will vary somewhat with voltage). You have given the cap value as 1 f and also .1 f. If a 1F the time constant will be 7.5secs, or 0.75 sec for a .1F<p>You will not get an LED to light at 1.5v - you would need to charge the cap to about 6v.

Gorgon
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Re: a circuit exhibiting exponential decay ??

Post by Gorgon » Fri Jun 10, 2005 4:04 pm

The main question in this is: Does the flashlight lamp work with the single 1.5V cell at all? Your connection does not increase the voltage with the capacitor, so do you have light when you connect the lamp over the battery?
I've always used at least 2 x 1.5V cells (3V) in my flashlights.<p>(But we have 230 VAC mains too. :D )<p>TOK ;)
Gorgon the Caretaker - Character in a childrens TV-show from 1968. ;)

Robert Reed
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Re: a circuit exhibiting exponential decay ??

Post by Robert Reed » Fri Jun 10, 2005 5:49 pm

Gorgon has a good point.
One other thing to remember in your calculations- is that in one time constant, the initial charged voltage will drop to 37% of its original value.Your indicator lamp may drop out prior to this point in time, so you may want to factor minimum lamp voltage into your equation. A double stacked capacitor? `Splain.

jimandy
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Re: a circuit exhibiting exponential decay ??

Post by jimandy » Fri Jun 10, 2005 5:54 pm

Seems I recall the resistance of an incandescent lamp is non-linear, i.e. low when cold and increasing as it begins to glow.
"if it's not another it's one thing."

rshayes
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Re: a circuit exhibiting exponential decay ??

Post by rshayes » Fri Jun 10, 2005 7:24 pm

The resistance of a lamp is not only nonlinear with voltage, but the light output is even more nonlinear with voltage. A light bulb would not be very predictable and would only indicate over a narrow voltage range.<p>LEDs have the same problem, they are nonlinear and they will shut off abruptly somewhere above 1 volt.<p>A resistor in the 10 ohm range would give you a 10 seco9nd time constant. This would be slow enough that the changes would be understandable. The best indicator might be an analog meter, since this would show the changes in rate without having to interpret a sampled display such as a digital voltmeter.<p>Radio Shack may still sell an analog meter that would work for this. It was basically a 1 milliamp meter with a 15K multiplier resistor to get a 15 volt range. Using a 1.3K resistor instead would give a full scale range of somewhere between 1.4 and 1.5 volts, depending on the meter resistance. A capacitor of about 6800 uF would give you close to a 10 second time constant.

Robert Reed
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Re: a circuit exhibiting exponential decay ??

Post by Robert Reed » Fri Jun 10, 2005 9:20 pm

While we are on the subject of capacitors and time constants, heres a good trivia question for you. An ideal capacitor of 1 MFD is placed across a voltage sorce of 10 volts-- how long does it take for full charge? Answer--beyond infinity. Since a capacitor can only charge ~63% of the remaining supply voltage in each time constant, in theory it will never make it to its 10 volt supply.
It will always be seeking that last smidgeon of voltage that it did'nt quite make it to in the time constant preceding it.

pebe
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Re: a circuit exhibiting exponential decay ??

Post by pebe » Sat Jun 11, 2005 1:51 am

A hypothetical question can only yield a hypothetical answer.<p>If by 'voltage source of 10 volts' you mean a fixed 10v voltage source - as distinct from a current source - then the source will have a zero source resistance, and the timeconstant will be zero. On that basis the capacitor will charge to full voltage instantly.<p>How long is 'beyond infinity'? :)

Gorgon
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Re: a circuit exhibiting exponential decay ??

Post by Gorgon » Sat Jun 11, 2005 4:57 am

Hi Pebe,
In this case I think your hypothetical fuse will blow instantly (or close to), because of the hypothetical current soaring to infinity. I suppose you use a capacitor with a hypothetical internal resistance of zero ohm. :D <p>And Joesplink:
To be serious, the 10 volts in this example is better than the 1.5 volt used before. In a practical world, use a 4.5 volt flashlight battery to perform the experiment. I think you will overcome most of the obstacles mentioned in here.<p>TOK ;)
Gorgon the Caretaker - Character in a childrens TV-show from 1968. ;)

Robert Reed
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Re: a circuit exhibiting exponential decay ??

Post by Robert Reed » Sat Jun 11, 2005 10:03 am

The capacitor is IDEAL, the 10 volt source is real world. I know this is a lot of nonsense, but I just thought it would get the gray matter stirring in some of you.

Gorgon
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Re: a circuit exhibiting exponential decay ??

Post by Gorgon » Sat Jun 11, 2005 10:22 am

Hi Robert,
I suppose your mission is completed, with success. :D But I still think the fuse blew!<p>TOK ;)
Gorgon the Caretaker - Character in a childrens TV-show from 1968. ;)

Robert Reed
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Re: a circuit exhibiting exponential decay ??

Post by Robert Reed » Sat Jun 11, 2005 3:46 pm

Maybe that was the reason the capacitor never fully charged.

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