7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

1/18

EMF and Internal

Resistance

Electricity Lesson 8

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

2/18

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.

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

3/18

Question

What is the dierence between emfand potential dierence?

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

4/18

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

5/18

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=

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

6/18

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.

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

7/18

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.

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

8/18

Circuit iagram

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

9/18

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. )

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

10/18

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

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

11/18

Including internalresistance

The resistors areconnected in series.

-o total resistanceis!7

6 r

$urrent throughthe cell!7

rRI

+

=

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

12/18

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 +=

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

13/18

Lost pd

The terminal pdcan be calculatedusing!7

The e9uationbecomes!7

The lost pd can becalculated using!7

Irv =IRV =

vVIrIR +=+=

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

14/18

&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?

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

15/18

&or'ed E(ampleiagram

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

16/18

)tep *

Treat the circuit as a perfect battery inseries with an internal resistor. Thecircuit becomes!

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

17/18

&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

7/25/2019 Electricity - Lesson 8 - EMF and Internal Resistance

18/18

&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.