1. Internal Resistance and the EMF of a cell
6th October 2016
IFP
(this replaces Lecture 4 on Learnzone)

2. First – recap on Meters

3. Could you start your car…
from a torch battery?

5. EMF – definition
EMF (Electromotive Force) is the energy per unit charge transferred into electrical energy by the battery.
Units – volts

6. Laptop on your lap
What do you notice?
Why?

7. Real batteries
ALL batteries have some “Internal Resistance” – the chemicals in the battery use up some of the energy before it gets to the battery terminals.
We model a battery as a “Perfect” battery joined in series to a fixed value resistor.
This is called the internal resistance and has symbol r.
Anything connected to the outside world we call the Load Resistance, symbol R. This can change.

8. As a diagram

9. So what?
Total emf supplied =current * total resistance ε = I (R + r). r and ε are fixed. As we vary the load, R, what happens? Two extremes – High Load and Low Load. At HIGH R… At LOW R… Note that internal resistance r will limit the current available – even if the load resistance is zero

10. Doing the math …
Total emf supplied =current * total resistance ε = I (R + r) ε = IR + Ir Since V = IR, we can rewrite both of these ε = V + v
Terminal p.d.
Lost Volts

11. And finally we can rearrange as
ε = V + v
V = ε – v
V = ε – Ir or
V = – Ir + ε
In this equation, V will vary as I varies. r and ε are constant.
Does this remind you of anything in maths?

12. The Graph
V = – Ir + ε
y = mx + c
p.d. / V
Current / A

13. If we want the emf of a cell (accurately), why can’t we just use a voltmeter?
Think about the circuit
For the voltmeter to work, it must pass a (small) current
So we have some lost volts
BUT we can create the graph and extrapolate to find the true value of ε

14. Worksheet – the story so far
Let’s try it – simple circuit, adjustable load, take readings of terminal pd and current. Draw a graph also.
Possibly data logging?

15. Back to our extremes
What is the effect of having a fixed value of internal resistance?
So how do you build a system that will deliver a high current?
MUST HAVE LOW INTERNAL RESISTANCE!

17. Car Starter Motor Needs about 120A. Battery has emf 12V
Let’s assume the starter motor resistance is 0.04Ω
What is the maximum value the internal resistance can have?

18. So which one?

20. Summary questions
EMF is the ______ transferred (into / out of) the current
EMF is measured in _____
All batteries have ________ _________
Why can’t we just measure EMF with a voltmeter?
A graph of terminal p.d. against current has a gradient of ___ and a Y intercept of the ____

21. For maximum power transfer, ________
Where is a low internal resistance vital? _______________
Where is a high internal resistance vital? _______________________

22. Problem Sheet 3 - complete