introduction to voltage

8/15/2019 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

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introduction to voltage