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Transcript of introduction to voltage
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ntroduction
Voltage (PD and EMF)
In the circuit below, several cells have been linked in a line to form a battery. The potential difference
(PD) across the battery terminals is 1 volts (!). This means that each coulomb (") of char#e will
$spend% 1 &oules of ener#y in movin# round the circuit from one terminal to the other.
'i#ure 1 1
The PD across the bulb is also 1 !. This means that, for each coulomb pushed throu#h it, 1 * of
electrical ener#y is chan#ed into other forms (heat and li#ht ener#y).
PD may be measured usin# a voltmeter as shown above.
PD, ener#y, and char#e are linked by this e+uation
-ner#y transformed char#e / PD
'or e/ample, if a char#e of " moves throu#h a PD of 0 !, the ener#y transformed is *.
The volta#e produced by the chemical reactions inside a battery is called theelectromotive
force (-2'). 3hen a battery is supplyin# current, some ener#y is wasted inside it, which reduces the
PD across its terminals. 'or e/ample, when a torch battery of -2' 0.4 ! is supplyin# current, the PD
across its terminals be mi#ht be only . !.
15.1 Internal resistance
(a) e/plain the effects of internal resistance on the terminal potential difference of a battery in a circuit5
Internal resistance
In reality, when a battery is supplyin# current, its output PD is less than its -2'. The #reater the current,
the lower the output PD. This reduced volta#e is due to ener#y dissipation in the battery. In effect, the
battery has internal resistance. 2athematically, this can be treated as an additional resistor in the circuit.
'i#ure 1
The battery above is supplyin# a current I to an e/ternal circuit. The battery has a constant internal
resistance r.
'rom 6irchhoff%s second law
7ut , so
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8o 99999(1)
'i#ure 1 0
The #raph above shows how ! varies with I . :nlike earlier #raphs, ! is on the vertical a/is.
;ote
< 3hen I is =ero, . In other words, when a battery is in open circuit (no e/ternal circuit), the PD
across its terminals is e+ual to its -2'
< 3hen > is =ero, ! is =ero. In other words, when the battery is in short circuit (its terminals directly
connected), its output PD is =ero. In this situation, the battery is deliverin# the ma/imum possible
current, , which is e+ual to . ?lso, the battery%s entire ener#y output is bein# wasted internally
as heat.
< ?s , it follows that . 8o the #radient of the #raph is numerically e+ual to the internal
resistance of the battery.
If both sides of e+uation (1) are multiplied by I , the result is . >earran#ed, this #ives the
followin#
'i#ure 1 @
Example 15.1
15. !irc""off#s la$
(b) state and apply 6irchhoff s laws5
Introduction
'i#ure 1
1. 'i#ure 1 shows three typical circuit dia#rams that mi#ht need to be solved (e.#. #iven the
resistances of all the resistors and the volta#es of all the batteries, find all of the currents). 'i#ure 1
(a) can be solve easily usin# %"m#s &a$, but (b) and (c) cannot be solved usin# the same law. Instead,
we must write down !irc""off#s la$sand solve the e+uations.
!irc""off#s first la$ (!F&)
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'i#ure 1
*unction is a point where two or more conductor meet to#ether.
The currents at &unctions A and B above illustrate a law which applies to all circuits
6irchhoff%s first law
The al#ebraic sum of currents in a network of conductors meetin# at a point is =ero
It arises because, in a complete circuit, char#e is never #ained or lost. The &unction rule is based on
the conservation of the electric charge . 8o the total rate of flow of char#e is constant. This means that
Cet%s consider
"urrent *unction
'i#ure 1
Positive Direction
;e#ative Direction
:sed 6irchhoff%s 'irst Caw
!irc""off#s second la$ (!'&)
-ner#y, work and -2'
1. 3hen we discuss about the 68C we have to represent the -2' in term of ma#nitude and direction
inside the circuit. The -2' device always keeps one of their terminal labeled $E% at hi#her electric
potential than labeled $%. This will present in arrow dia#ram as
'i#ure 1 F
. when connected to the circuit, -2' will causes a net flow of positive char#e from positive terminal to
ne#ative terminal in the same direction as -2', this flow is part of current. The flows of current throu#h
the load (resistor) within the circuit will made the -2' drop this concept name as voltage drop. The
direction of the volta#e drop oppose the current flow.
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'i#ure 1 G
'i#ure 1 14
The arran#ement above is called $a circuit%. 7ut, really, there are two complete circuits throu#h the
battery. To avoid confusion, these will be called loops.
Cets consider
losed &oops
Parallel 'eries
'i#ure 1 11
Coop 1 and Coop can be form
'i#ure 1 1
Coop 1
In the circuit above, char#e leaves the battery with electrical potential ener#y. ?s the char#e flows round
a loop, its ener#y is $spent% H in sta#es H as heat. The principle that the total ener#y supplied is e+ual to
the total ener#y spent (conservation of energy) is e/pressed by 6irchhoff%s second law.
6irchhoff%s second law>ound any closed loop of a circuit, the al#ebraic sum of the -2's is e+ual to the al#ebraic sum of the
PDs (i.e. the al#ebraic sum of all the I>s).
This would means that
;ote
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'or e/ample, in the circuit below, it%s assume that the current is flow in counter clock wise, the -2' of
the ri#hthand battery is taken as ne#ative (@ !) because it is opposin# the loop direction and the
volta#e drop is positive because it%s oppose to the loop direction, therefore
'i#ure 1 10
(a) ?l#ebraic sum of -2's 1F E (@) E1@!
(b) ?l#ebraic sum of I>s (!olta#e drop) ( / 03) E ( / @3) E1@ !
?pplyin# the second 6irchhoff%s law the e+uation will be
esistors in parallel
'i#ure 1 1@
'rom 6irchhoff%s second law (applied to the various loops)
- I> (Coop with total >esistor)
and- I1 >1 (Coop with >esistor >1)
and
- I > (Coop with >esistor >)
'rom 6irchhoff%s first law I I1 E I.
8o
esistors in seriesIf >1 and > below have a total resistance of > then > is the sin#le resistance which could replace them.
'i#ure 1 1
'rom 6irchhoff%s first law, all parts of the circuit have the same current throu#h them because there is
only one input and one output
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'rom 6irchhoff%s second law
- I> and - I>1 E I>.
8o I> I>1 E I>
J >>1E>
'or e/ample, if >1 0 3 and > 3, then > G 3.
Example 15.15.* Potential divider
(c) e/plain a potential divider as a source of variable volta#e5
(d) e/plain the uses of shunts and multipliers5
Potential divider
a volta#e divider (also known as a potential divider) is a linear circuit that produces an output volta#e
(V out) that is a fraction of its input volta#e (V in)
? potential divider or potentiometer like the one below passes on a fraction of the PD supplied to it.
'i#ure 1 1
In the input loop above, the total resistance >1 E >.
8o
7ut !out I>,
so
;ote
. If such a circuit is
connected, then the output PD is reduced.
In electronics, a potential divider can chan#e the si#nals from a sensor (such as a heat or Ii#ht.detector)
into volta#e chan#es which can be processed electrically. 'or e/ample, if > is a thermistor, then a rise
in temperature will cause a fall in > and therefore a fall in !out. 8imilarly, if > is a li#htdependent
resistor (CD>), then a rise in li#ht level will cause a fall in >, and therefore a fall in !out.
Potential dividers are not really suitable for hi#hpower applications because of ener#y dissipation
'"unt and multiplier (a) "onversion of Kalvanometer to ammeter
'i#ure 1
8hunts
8hunts is a resistor connected in parallel
8ince
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(b) "onversion of Kalvanometer to voltmeter
'i#ure 1 0
15.+ Potentiometer and ,"eatstone -ridge
(e) -/plain the workin# principles of a potentiometer, and its uses5
(f) -/plain the workin# principles of a 3heatstone brid#e, and its uses5
(#) 8olve problems involvin# potentiometer and 3heatstone brid#e.
Potentiometer
Potentiometer is an instrument that can be used to measure the emf of a source without drawin#
(considerin#) any current from the source.
Function To measure emf a cell
6ey Idea make sure the #alvanometer as a null detector
'i#ure 1 @
E = lV
where
V potential difference per unit len#th of ?7.
L The len#th of wire
l len#th that #alvanometer show =ero readin#
so PD across l ,
Potentiometer /pplications
(a) 2easurin# a cell%s internal resistance.
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'i#ure 1
or
'i#ure 1
If a #raph is plotted,
Kradient,
Internal resistance,
Intercept,
(b) "omparin# resistance
'i#ure 1
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,"eatstone -ridge
1. ? ,"eatstone -ridge is an electrical circuit used to measure an unknown electrical resistance by
balancin# two le#s of a brid#e circuit.
. ? brid#e circuit is a type of electrical circuit in which two circuit branches (usually in parallel with each
other) are Lbrid#edL by a third branch connected between the first two branches at some intermediate
point alon# them
'i#ure 1 F. (a) a parallel circuit , (b) a 7rid#e circuit
0. a ratio between resistance #iven by