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7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance
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EMF and Internal
Resistance
Electricity Lesson 8
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Learning Objectives
To know why the pd of a cell in useis less than its emf.
To know how to measure the internalresistance of a cell.
To know how to calculate how muchpower is wasted in a cell.
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Question
What is the dierence between emfand potential dierence?
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Answer
Emf is the total energy supplied tothe circuit per unit charge by thesource.
pd is the energy per unit chargeconerted to other energies by thecomponents.
7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance
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Electromotive Force
The energy supplied to a circuit by a battery isgien by!
Wis the energy in "# Qis the charge in $# % is theemf in olts &'(T 'ewtons).
'o circuit at all is *++ , eicient. -ome energyis dissipated in the wires# or een in the batteryitself.
Q
E=
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Internal Resistance
The internal resistance of a source is theloss of potential dierence per unitcurrent in the source when current
passes through the wire.
t is caused by the opposition to the /owof charge through the source.
We will use the symbol r to representinternal resistance.
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Terminal pd
The electrical energy per unit chargedeliered by the source when it is in acircuit.
The terminal pd# 0# is less than the emf# %#wheneer current passes through thesource.
The dierence is the lost pd# # due to theinternal resistance of the source.
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Circuit iagram
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A simple circuit!
n this circuit theoltmeter reads &erynearly) the emf.
&1 per"ect voltmeterhas in#niteresistance. 1 digitalmultimeter has aver$
%ig%resistance# soneeds a tiny current2it is almost perfect. )
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Add a resistor!
This time we 3nd thatthe terminal oltagegoes down to V.
-ince 0 is lessthanE#
this tells us that not allof the oltage is beingtransferred to theoutside circuit2 some islost due to the internal
resistance which heatsthe battery up. Emf 4 5seful olts 6
Lost olts
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Including internalresistance
The resistors areconnected in series.
-o total resistanceis!7
6 r
$urrent throughthe cell!7
rRI
+
=
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Lost pd
-o the cell
n other words!7
n energy terms the lost pd is the energyper coulomb dissipated or wasted insidethe cell due to the internal resistance.
IrIRrRI +=+= )(
pdlost''thepdterminaltheemfcell +=
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Lost pd
The terminal pdcan be calculatedusing!7
The e9uationbecomes!7
The lost pd can becalculated using!7
Irv =IRV =
vVIrIR +=+=
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&or'ed E(ample
1 battery of emf *: olts andinternal resistance +.; ohms isconnected to a *+ ohm resistor.
What is the current and what is theterminal oltage of the battery underload?
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&or'ed E(ampleiagram
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)tep *
Treat the circuit as a perfect battery inseries with an internal resistor. Thecircuit becomes!
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&or'ed )olution
)tep +, Work out the total resistance
tot 4 * 6 : 4 *+ ohms 6 +.; ohms 4*+.; ohms
)tep -,'ow work out the current! 40 1
)tep .,work out the oltage across theinternal resistor &lost oltage)! 4 r 4*.*> amps +.; ohms 4 +.;@ olts
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&or'ed )olution
-tep ;! work out the terminal oltage!Terminal oltage 4 emf 7 lost oltage4 *: 7 +.;@ 4 **/.- volts
We can of course work out theterminal oltage by working the
oltage across the *+ ohm resistor#assuming there are no losses.