Today`s Objectives - RanelaghALevelPhysics
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Transcript Today`s Objectives - RanelaghALevelPhysics
EMF and Internal Resistance
Electricity Lesson 9
Learning Objectives
To know why the pd of a cell in use is less than
its emf.
To know how to measure the internal resistance
of a cell.
To know how to calculate how much power is
wasted in a cell.
Question
What is the difference between emf and
potential difference?
Answer
Emf is the total energy supplied to the
circuit per unit charge by the cell.
pd is the energy per unit charge converted to
other energies by the components.
Electromotive Force
The energy supplied to a circuit by a cell is given by:
E
Q
E is the energy in J, Q is the charge in C, ε is the emf in
volts (NOT Newtons).
No circuit at all is 100 % efficient. Some energy is
dissipated in the wires, or even in the cell itself.
Internal Resistance
The internal resistance of a source is the loss of potential
difference per unit current in the source when current
passes through the wire.
It is caused by the opposition to the flow of
charge through the source.
We will use the symbol r to represent internal
resistance.
A simple circuit…
In this circuit the
voltmeter reads (very
nearly) the emf.
(A perfect voltmeter
has infinite
resistance. A digital
multimeter has a very
high resistance, so needs
a tiny current; it is almost
perfect. )
Add a resistor…
This time we find that the
terminal voltage goes down
to V.
Since V is less than E, this
tells us that not all of the
voltage is being transferred to
the outside circuit; some is
lost due to the internal
resistance which heats the
battery up.
Emf = Useful volts + Lost
volts
Terminal pd
The electrical energy per unit charge delivered
by the source when it is in a circuit.
The terminal pd, V, is less than the emf, ε,
whenever current passes through the source.
The difference is the lost pd, v, due to the
internal resistance of the source.
Including internal resistance
The resistors are
connected in series.
So total resistance is:R+r
Current through the
cell:-
I
Rr
Lost pd
So the cell
I ( R r ) IR Ir
In other words:-
cell emf the terminal pd the ' lost' pd
In energy terms the lost pd is the energy per coulomb
dissipated or wasted inside the cell due to the internal
resistance.
Circuit Diagram
Lost pd
The terminal pd can be
calculated using:-
V IR
The lost pd can be
calculated using:-
v Ir
The equation becomes:-
IR Ir V v
Worked Example
A battery of emf 12 volts and internal resistance
0.5 ohms is connected to a 10 ohm
resistor. What is the current and what is the
terminal voltage of the battery under load?
Worked Example Diagram
Step 1
Treat the circuit as a perfect battery in series with an
internal resistor. The circuit becomes:
Worked Solution
Step 2: Work out the total resistance
R tot = R1 + R2 = 10 ohms + 0.5 ohms = 10.5
ohms
Step 3: Now work out the current:I = V/R =
12 ÷ 10.5 = 1.14 A
Step 4: work out the voltage across the internal
resistor (lost voltage): v = Ir = 1.14 amps × 0.5
ohms = 0.57 volts
Worked Solution
Step 5: work out the terminal voltage: Terminal
voltage = emf - lost voltage = 12 - 0.57 = 11.43
volts
We can of course work out the terminal voltage
by working the voltage across the 10 ohm
resistor, assuming there are no losses.
Power Wasted in a Cell
Recall that power can be calculated using:-
P IV
IR Ir
So we can multiply our equation by I to get:Power supplied, I I R I r
2
2
Or in words:Power supplied by the cell
Power delivered to R Power wast ed in the cell
Measuring Internal Resistance
Measuring Internal Resistance
Terminal pd and current can be plotted on a
graph.
V v
V v
V Ir
This equation is in the form of a straight line
V rI
y mx c