NOTES FOR THE INVESTIGATION INTO THE EMF AND INTERNAL RESISTANCE OF CELL

  1. I assume that you have some idea what ‘emf E’ and ‘internal resistance r’ of a cell mean.
  2. The basic circuit enables you to record triplets of values of V, I, and R.  You should realise by now that E = V + Ir.  This means that the emf of the cell is the sum of the voltage it is supplying outside itself (its ’terminal voltage’) added to the voltage that is being wasted in the internal resistance, inside the cell (the ‘lost volts’)
  3. Prediction/Explanation:  Why does the terminal voltage reduce as the external resistance reduces?  (And why, by the way, does it reduce much more when the external resistance changes from 2 W to 1 W than it does when the resistance changes from 9 W to 8 W?

PHASE 1

  1. If E stays the same as you take more current from the cell, then you can assume that V1 + I1 r= V2 + I2 r.  Therefore, using any two adjacent pairs of readings of V and I, you can calculate r.  Obtain an algebraic formula for r.
    1. Is there any point in taking non-adjacent pairs of readings?
  2. Still assuming that E stays the same, do you get the impression that r changes as you take more current from the cell?
    1. Prediction:  Do you think, given what you know about resistance, that r is likely to remain constant as I changes?  Why shouldn’t it?  If it doesn’t stay constant, how might it change, and why?
  3. Conclusion:  Plot a graph of r against the average current Iav. (Using adjacent values of I, obviously).  Assuming E is constant, how do you think r may be varying with I  Is it perhaps staying constant?
    1. Evaluation:  To test this, you need to get an impression of the reliability of your data.

                                                               i.      Firstly, you should consider the inaccuracy in your current and voltage readings.  Try the effect on a best r, in a typical pair of cases, of making small alterations (+ or - ) in the quartet of values I1 I2 V1 V2; make sure you have devised the most unlucky case – the one that makes r as large it could possibly have been.  How different is this “error value” from your “best value”?  Looking at it, could any variation in r you obtained just be the result of inevitable experimental inaccuracy?

                                                             ii.      Secondly, you should investigate how repeatable your results are.  Maybe any variation you are getting in r is caused by the cell running down, rather than by it supplying more current.  Once the cell has been supplying a large current, does it give the same readings that it gave before, when you go back to a small current?  In other words, does the short-term history of the cell make a difference to your readings?  (We know that the long-term history makes a difference…)

PHASE 2

  1. It is not satisfactory to remain unsure whether our assumption that E is remaining constant is accurate.   It is a crucial assumption.  Explain why.
  2. To test this assumption, we need to use a more sophisticated mathematical analysis, based on the equation already stated.  If E = V + Ir then we know that   V = - Ir + E.  Reordering, we get V = -r I + E.  Compare this with the general equation for a straight line: Y = mX + c.  If we plot a graph of V against I, its shape will be a severe test of the constancy of both E and r:  If E and r are both constant, then V = -r I + E is in fact the equation of a straight descending line, whose gradient is r and whose y-intercept is E.
  3. Concluding:  Plot the graph.  What do you think?
  4. Evaluating:  Could the ± variation away from a straight line be caused by experimental inaccuracy?  Find out what the ± inaccuracy on each data point would look like plotted as an error bar.  Could a straight line now go through all the data point error bars?

PHASE 3a

  1.   If you think that there may be some change – even a small change - in either E or r as I increases, you have an interesting investigative problem: if, say, E decreased as I increased, this would produce the same effect on V as if r increased as I increased.  In both cases, though for different reasons, V would decrease more than it would if E and r are both constant.  Explain why.
  2.   Is there any way of getting around this problem?  I’m inclined to think that there isn’t.  Maybe you could do a search on the Internet to see if there is some interesting information.

PHASE 3b

  1.   Prediction/Explanation:  Obtain as much background knowledge as you can about emf and internal resistance.  After all, a dynamo spinning at a constant rate will generate a constant E, and will have a constant r, regardless of how much current it supplies (Explain).  Does it seem reasonable that a cell behaves in the same way?