Can the Slope of a Graph Determine EMF and Internal Resistance?

In summary, the slope of voltage vs. current is resistance, and the gradient is the slope is the derivative for straight lines.
  • #1
mininirime
4
0
I'm doing a few practicals at home this summer, and the one that is bugging me is about EMF. I have measured voltage and current at different resistances across a 4,5 V battery, and made a graph. But to find the emf, am I supposed to take the slope of the graph, or the gradient? Or is that the same, aka the derivative? English isn't my first language, but I go to an English school, so...

My graph gives a function y=-1,26x + 5,772. Is it possible for the slope to be negative, and thus the emf? I have current at x-axis and voltage at y-axis.

Thanks for all the help, I hope this doesn't seem like I want you to do my homework for me ^^o:)
 
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  • #2
The slope of voltage vs. current is resistance, as given by the equation: V=IR The gradient is the slope is the derivative for straight lines

I don't see how you could have gotten a negative slope. But then again, I don't see how your voltage is capable of varying on a 4.5 volt battery.
 
  • #3
this is why Electricity is my least favourite part of physics :grumpy:

No, the battery is 4.5 volts, which measn that the perfect emf is 4,5 volts, right? And then I vary the length of resistance, or the wire, from 100 cm to 5 cm. I measure the potential difference and current, and plot those two... so the voltage shrinks because the resistance gets bigger. does that make sense?
e=rI + V <- I'm supposed to be using this.
Maybe the slope is negative because I plotted the biggest resistance results first, and then the smaller resistance results. This would mean that the highest voltage values would come first...
 
  • #4
The internal resistance of the cell is the "negative" of the slope when
plotting V vs I. V = E - IR where V is the ordinate (y-axis and I is
the abcissa (x-axis).
 
  • #5
Thanks, I plotted V along y-axis and I along X-axis. But to find the internal resistance r, should I use the formula V=Ir, or does that only work for "external" resistances? Because I can only use the V=E-Ir with one unknown, and currently the r is sort of unknown. Or I am blind and/or stupid :p

I really appreciated the help ;)
 
Last edited:
  • #6
mininirime said:
Thanks, I plotted V along y-axis and I along X-axis. But to find the internal resistance r, should I use the formula V=Ir, or does that only work for "external" resistances? Because I can only use the V=E-Ir with one unknown, and currently the r is sort of unknown. Or I am blind and/or stupid :p

I really appreciated the help ;)
Okay, you've plotted your graph correctly, now compare your equation (in a slightly re-arranged form) with the standard equation of a straight line;

V = -rI + E
y = mx + c


Note, that here voltage is on the y-axis and current is plotted on the x axis. Which letter is r equivalent to in the second equation and what does this letter represent?
 
  • #7
well, when you put it that way... It makes much more sense ;) I've managed to find the internal resistance and E now! I think it's about seing the connections... which I'm really not that good at :s but thanks for the help!
 
  • #8
mininirime said:
I think it's about seing the connections... which I'm really not that good at :s but thanks for the help!
That will come, in time. My pleasure.
 

1. What is EMF and how does it relate to internal resistance?

EMF stands for Electromotive Force and it is the measure of the energy that causes electric current to flow in a circuit. It is often confused with voltage, but they are not the same. Internal resistance, on the other hand, is the resistance to current flow within a battery or power source. EMF and internal resistance are related in that the internal resistance affects the amount of current that can be drawn from the EMF.

2. How does internal resistance affect the performance of a battery?

The internal resistance of a battery affects its overall performance by decreasing the amount of current that can be drawn from it. This means that as the battery is used, its voltage decreases due to the internal resistance, and it may not be able to power devices that require high currents. The internal resistance also causes the battery to heat up, reducing its lifespan.

3. Is there a way to measure the internal resistance of a battery?

Yes, there are various methods to measure the internal resistance of a battery. One way is to use a multimeter and measure the voltage drop across the battery while a known current is flowing through it. The internal resistance can then be calculated using Ohm's Law (R=V/I). Another method is to use a battery analyzer, which can provide a more accurate measurement of the internal resistance.

4. How can internal resistance be reduced?

Internal resistance cannot be completely eliminated, but it can be reduced. One way to reduce internal resistance is by using a larger battery with more cells connected in parallel. This increases the surface area of the electrodes and reduces the overall resistance. Another way is to use batteries with lower internal resistance, such as lithium-ion batteries, which have a lower internal resistance compared to lead-acid batteries.

5. Can EMF and internal resistance be affected by external factors?

Yes, external factors such as temperature and age of the battery can affect both EMF and internal resistance. High temperatures can increase the internal resistance of a battery, reducing its performance. Aging of the battery can also increase its internal resistance, causing a decrease in EMF and overall performance. It is important to store and use batteries in optimal conditions to minimize the effects of external factors.

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