Transcript Internal Resistance

Internal Resistance
and
the EMF of a cell
6th October 2016
IFP
(this replaces Lecture 4 on
Learnzone)
Objectives
First – recap on Meters
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
Could you start your car…
from a torch battery?
Objectives
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
EMF – definition
• EMF (Electromotive Force) is
the energy per unit charge
transferred into electrical
energy by the battery.
• Units – volts
Objectives
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
Objectives
Laptop on your lap
• What do you notice?
• Why?
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
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.
Objectives
As a diagram
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
Objectives
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…
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
At LOW R…
Note that internal resistance r will limit the current
available – even if the load resistance is zero
Key Words
Emf, internal
resistance, Load
resistance.
Objectives
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
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
Objectives
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?
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
Objectives
The Graph
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
V = – Ir + ε
y = mx + c
p.d. / V
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Current / A
Key Words
Emf, internal
resistance, Load
resistance.
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
Objectives
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
Objectives
• Define EMF and
internal resistance
• Worksheet – the story so far
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Let’s try it – simple circuit,
adjustable load, take readings of
terminal pd and current. Draw a
graph also.
• Possibly data logging?
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
Objectives
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!
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
Objectives
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
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?
So which one?
Summary questions
1. EMF is the ______ transferred
(into / out of) the current
2. EMF is measured in _____
3. All batteries have ________
_________
4. Why can’t we just measure EMF
with a voltmeter?
5. A graph of terminal p.d. against
current has a gradient of ___ and
a Y intercept of the ____
Objectives
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
Objectives
• Define EMF and
internal resistance
6. For maximum power transfer,
________
7. Where is a low internal
resistance vital?
_______________
8. Where is a high internal
resistance vital?
_____________________
__
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.
Objectives
Problem Sheet 3 - complete
• Define EMF and
internal resistance
• Show that Terminal
Potential Difference
changes as external
resistance changes
• Use a graph to
determine EMF and
internal resistance
• Know how to
maximise Power
transfer
Key Words
Emf, internal
resistance, Load
resistance.