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Anyone from the NE KS regional have any opinions about the Shock Value event that was held there? thanks

Slothface wrote:Hey I'm a little bit confused about the whole 'internal resistance of a battery' concept. Can anybody help me out?

The way I understand it is it is effectively the limit to the current a battery can produce. Such as if a battery was 10V and had 1 Ohm of internal resistance, you could short circuit it and only produce a 10 ohm current, where it would be extremely high if the battery did not have internal resistance, and I think it also adds the resistance to all circuits.

Schrodingerscat wrote:

Slothface wrote:Hey I'm a little bit confused about the whole 'internal resistance of a battery' concept. Can anybody help me out?

The way I understand it is it is effectively the limit to the current a battery can produce. Such as if a battery was 10V and had 1 Ohm of internal resistance, you could short circuit it and only produce a 10 ohm current, where it would be extremely high if the battery did not have internal resistance, and I think it also adds the resistance to all circuits.

Thanks a bajazillion!!!!!M

Slothface wrote:Hey I'm a little bit confused about the whole 'internal resistance of a battery' concept. Can anybody help me out?

From what I know, every object (except for superconductors) has resistance and this includes batteries. Therefore, the internal resistance of a battery is the resistance of the materials that the batteries are made of, and this resistance can be altered by the placement of the cells in the battery. For more information, I would recommend going to http://www.allaboutcircuits.com

On this topic of batteries and resistance: A battery can be modeled (rather well) as a voltage source, in series with a small resistor. Because of this when you add batteries(or cells) in series you increase this resistance and when you add them in parallel you decrease this resistance. This general idea is how batteries in your car while only at 12V can supply very large amounts of current (Does anyone know how car batteries start your car?), and why shorting a car battery is a much worse idea then shorting a AAA battery which has a much higher resistance.

As a note, almost all components have some sort of resistance in series, and in parallel with the ideal component (except ie.superconductors). So a better model for a battery would have some resistance in parallel with the battery, but this resistance is very large which means it does not play much of a role in many circuits, it does play some role in draining your battery over time though! Another thing to point out is that the resistance of batteries changes dramatically as they discharge, which is why you can't draw many amps from a battery that is almost dead.

Another interesting problem you might want to try is this: If you have a battery that supplies a voltage of V and has a internal resistance of r, what value resistor R do you hook up in series with the battery to get the maximum power dissipation across the resistor R

Hmm, I got the power dissipated to be

How would you find the maximum? The three variable expression looks pretty complicated. But we can just ignore the though.

JSGandora wrote:Hmm, I got the power dissipated to be

How would you find the maximum? The three variable expression looks pretty complicated. But we can just ignore the though.

Very nice job setting up that part of the problem! Now, unfortunately the next step is sort of out of scope for (most*) middle schoolers (and of this event) but what you need to do is find the maximum of that function assuming that the Voltage and "r" are constants, or as you'll learn in calculus, take the derivative and set it equal to zero. Off the top of my head I can't think of any other methods to rigorously prove the answer (ie other then plug and chug). If you don't know how to take the derivative wolframalpha.com can help. Also good point with the , only the ratio of the resistors matters.

Another interesting question I have up my sleeve: You have one charged capacitor, Capacitance C, and with initial Voltage V, you hook it up to another discharged capacitor of Value C, What is the voltage across the new set of capacitors? Assuming they are perfect capacitors and hooked up by superconductors (you could in theory make capacitors out of superconductors), what happens to the excess energy? Where does it go?

*edited post to include (most) and the point with ratio of resistors, also even if you don't know anything about capacitors(which you don't have to) the second half of the question can be simplified to: if you have a short burst of current through a superconductor is any energy dissipated? How?

sean9keenan wrote:

JSGandora wrote:Hmm, I got the power dissipated to be

How would you find the maximum? The three variable expression looks pretty complicated. But we can just ignore the though.

Very nice job setting up that part of the problem! Now, unfortunately the next step is sort of out of scope for a middle schooler (and of this event) but what you need to do is find the maximum of that function assuming that the Voltage and "r" are constants, or as you'll learn in calculus, take the derivative and set it equal to zero. Off the top of my head I can't think of any other methods to rigorously prove the answer (ie other then plug and chug). If you don't know how to take the derivative wolframalpha.com can help.

This is exactly the way to get this, yes. When solved, however, we find that R=r - that the two resistances are equal. One can find this by doing what you mentioned - although it's a lot of ugly math to do so.

This is a general case, too. Always holds for internal resistance or a resistor in series with a voltage source. Somewhat important concept in source transformations (although I doubt this is a topic covered by the event).

Well, I don't know much about calculus but I'll take your word for it.

As for the capacitance problem, I only have a vague idea how to calculate capacitances mostly because the rules strictly say capacitors are not to be covered. Anyhow, I still occasionally wander into capacitor land.

JSGandora wrote:Well, I don't know much about calculus but I'll take your word for it.

As for the capacitance problem, I only have a vague idea how to calculate capacitances mostly because the rules strictly say capacitors are not to be covered. Anyhow, I still occasionally wander into capacitor land.

And yeah, the answer comes out to R=r. I attached the derivative of the function below, and when you set it to zero, you should easily see that R=r
http://www.wolframalpha.com/input/?i=De ... spect+to+R

Yeah, I sort of realized that capacitors were out of the scope after I posed the question... This question is still valid for shock value: If you have a short burst of current through a superconductor is any energy dissipated? Or my question of how car batteries start your car.