Resistor Color CodesLearn how to identify different resistors with their colour codeelectric circuit | education

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The humble resistor is a key component of many renewable energy systems. They are designed to resist electricity and can therefore be used to supply the correct voltage to the various components in an electric circuit.

Because resistors are so small - too small to print numerical resistance values on - they are instead marked with four, five, or (less commonly) six coloured bands. Each colour represents a different number and so the value (in Ohms) of the resistor can easily be calculated.

Resistor Colour Code Chart

The last coloured band is usually used to indicate the tolerance - a measure of how accurate the stated resistance is, i.e. 1%, 2%, 5%, or 10%. In the case of six band resistors, is used to show the temperature coefficient - a measure of how much the resistance of a resistor is changed by changes in temperature.

Remembering the Resistor Colour Code Values

There are many mnemonic phrases to help you to remember the order of the colours:Black Brown Red Orange Yellow Green Blue Violet Gray White...which correspond to the values 0-9. For example:Bad Beer Rots Our Young Guts But Vodka Goes Well.

Electric current

is a means by which electrical energy is transferred from one place to another for utilisation. Charges in

motion constitute an electric current.

We know from electrostatics that when an isolated conductor is placed in an electric field, the charges in the

conductor rearrange themselves so that the interior has no net electric field. This constitutes of a transient

current, that is a current of short duration. It ceases the moment the net electric field in the conductor

becomes zero.However , to maintain a steady current, a source of emf is needed. This and other aspects of current electricity, such as resistance, are discussed in this chapter

A current is any motion of charge from one region to another. The illustration below shows two bodies at

different potentials. When these are connected with a wire, free electrons flow from B to A until both bodies

attain the same potential, after which the current ceases to flow. Current flows if a potential difference exists

throughout a conductor. This branch of physics dealing with charges in motion is called current electricity.

The amount of charge flowing through a given cross-section of a conductor per unit time constitutes electric

current.

When a battery or a cell is connected across the ends of a conductor, the thus set up exerts a force on

the free

electron causing them to move as shown in the figure. The arrows give the direction of the conventional

current.

Current is a scalar quantity. The direction of conventional current in any circuit is the direction in which the

positive charges flow.

Mathematically, for a steady current across any area,

where I is the current, and q is the charge that flows across that area in time t.

The S.I. unit of current is Ampere (A).

One ampere of current is said to flow through a wire if at any cross section, one coulomb of charge flows in

one second.In solid conductors, the current carriers are the free electrons; in electrolytes, the anions and cations; and in

gases, the electrons and anions.

No current flows in a copper wire by itself, just as water in a horizontal tube does not flow. If one end of the

tube is connected to a tank with water such that there is a pressure difference between the two ends of the

horizontal tube, water flows out of the other end at a steady rate. The rate at which water flows out depends

on the pressure difference, for a given tube. If the flow rate (current) is to be kept constant, the water flowing

out for instance has to be put back into the jar to maintain the pressure head. This requires work to be done

by an external agency. The above analogy brings out several features of electrical current flow. An electric

current flows across a conductor only if there is an electric potential difference between its two ends. To

maintain a steady current flow, one needs an agency, which does work on the charges. This agency is

called the electromotive force or emf.

In the case of water flow, the agency is the pump 'P' which does work at a steady rate in putting the water

back into the tank. Just as for a given tube, the current of fluid flowing out depends on its viscosity, the

electrical current flowing for a given potential difference depends on the electrical resistance of the

conductor.

The above circuit diagram shows the flow of charges. A steady electric current 'I' flows through the resistance R, from A to B. That is, positive charges flow from higher potential (A) to lower potential (B). The potential drop from A and B is V. The source P of emf does work on these charges, as they come through at B because it has to take the positive charges from lower to higher potential. The charge is transferred from one end of the source of emf to the other and 'qV' work is done on the charge. The source of emf by doing

work on the electric charges, maintains a potential difference V between its terminals.

Ohm's Law

It is found experimentally that the current I flowing through a conductor is directly proportional to the

potential difference V across its ends, provided the physical conditions (temperature, mechanical strain,

etc.,) remain constant. That is

or V = IR

where R is the resistance of the conductor.

This equation, called Ohm's law, is named after G.S. Ohm who first discovered it in 1828. The unit of

resistance is Ohm (1W = 1VA-1). Ohm's law is only empirical. These conductors (e.g.; metals) which obey

Ohm's law are called Ohmic conductors.

If the material is not Ohmic, the relation between V and I is not linear, so that R is not constant. Still, R=V/I

serves as the definition of resistance.

Departures from Ohm's law are discussed in a later section. Resistivity

The resistance of a resistor depends on the nature of the material, its geometrical features (length and

cross-sectional area) and on the temperature and pressure. It is useful to separate out the dependence on

the geometrical factor.

Consider a rectangular slab of some conducting material, of length l and cross-sectional area A. If the length

is doubled (fig. (a)) for a fixed current I, the potential drop across the slab also doubles. (This is because the

potential difference is the electric field times the distance, and for a fixed current, the electric field that drives

it, stays the same).

 

 

Therefore, the resistance doubles on doubling the length. That is

Now, suppose that the slab is cut lengthwise into two parallel slabs (fig.(b)) each of area A/2. If the current

flowing through the full slab is I for a given voltage V, then the current flowing through each half -slab is I/2.

Therefore, the resistance of each half - slab is twice that of original full slab. But these two slabs differ only in

the cross - sectional area. Thus,

Combining (1) and (2), we get

where r, the constant of proportionality, is called resistivity. It depends only on the nature of the material and

its physical conditions. The unit of r is ohm m (Wm).

Material Nature Resistivity at room temp in ohm-metre

Copper Metal 1.7x10- 8

Iron Metal 9.68x10- 8

Manganin Alloy 48x10- 8

Nichrome Alloy 100x10- 8

Pure Silicon Semiconductor 2.5x 103

Pure Germanium Semiconductor 0.6

Glass Insulator 1010 to 1014

Mica Insulator 1011 to 1015

 

The reciprocal of resistance of a conductor is called its conductance (G). Therefore, G = 1/R. The S.I. unit of

conductance is mho or siemen (S).

The inverse of resistivity of a conductor is called its conductivity (s);

 

The S.I. unit of conductivity is siemen metre-1 (sm-1) or mho m-1 or (Wm)-1.

Good electrical conductors such as metals are usually good conductors of heat also. Insulators such as

ceramic and plastic materials are also poor conductors of heat.

In metals, the free electrons that carry charge in electrical conduction also provide the principal mechanism

for heat conduction.

Semiconductors

Semiconductors have resistivities intermediate between those of metals and insulators. They are important

because of the way they are affected by temperature and small amount of impurities.

Colour Code for Resistors

A resistor is a component in a circuit whose function is to provide a specified value of resistance. The

commonly used resistors are the carbon resistors made from powdered carbon mixed with binding material

and baked into a small tube with wire attached to each end. These have resistance values from a fraction of

an ohm to several million ohms.

Carbon resistors are marked with a set of co-axial coloured rings. An example is shown in the figure below.

These rings indicate the value of their resistance (the table gives the colour code) and the percentage

accuracy.

 

 

Equation

ColourNumber

In order to remember the colour code, the

following sentence may be helpful.

(Black) B

(Brown) B

(Red) R

(Orange)O

(Yellow) Y

(Green) G

(Blue) B

(Violet) V

(Grey) G

(White) W

0

1

2

3

4

5

6

7

8

9

BB Roy Great Britain Very Good Wife

 

The first two colour bands (i.e., A and B) from the end indicate the first two significant figures of the

resistance in ohms. The third colour band i.e., C indicates the decimal multiplier and the last band D stands

for the tolerance in percent about the indicated value. If this last band is gold, the tolerance is 5%, if silver it

is 10%. If it is absent, the tolerance is 20%.

Example: If ABCD represent colours yellow, violet, brown and gold respectively, the value of the resistance

will be

In electrostatic situations, the electric field is zero everywhere within the conductor, and there is no current.

This does not mean that all charges within the conductor are at rest. In metals such as copper or aluminium,

some of the electrons are free to move within the conducting material. These free electrons move randomly

in all directions with a speed of the order of 106 ms-1. But, the electrons do not escape from the material as

they are attracted to the positive ions of the material. Since the motion of the electrons is random, there is no

net flow in any direction and hence the current is zero.

When the same metal is in an electric field, the electrons are subjected to a steady force given by

If the electrons were moving in vacuum, the steady force would cause a steady acceleration in

the direction of� an the electrons speed would have gone up. But in a conductor, the electrons undergo

frequent collisions with the ions of the material. Hence, the direction of the electrons undergoes a random

change. See figure below, the net effect is that in addition to the random motion of the electrons, there is

also a very slow net motion or drift of the electrons. This drift or flow with a constant velocity (in a direction

opposite to ) is called the drift velocity VD.

 

To find the relationship between current and drift velocity, consider a conductor of length l and area of cross-

section A. If V is the potential difference across the ends of the conductor, then the strength of the electric

field is

The acceleration acquired by each electron due to the electric field is

where is the coulomb's force experienced by each electron and m is the mass of the electron.

The drift velocity of the electrons is given by

where t, the relaxation time, is the average time that an electron spends between two collisions. It is of the

order of 10-14 s.

Now the volume of the conductor is equal to Al and if n is the number of free electrons per unit volume, then,

the total number of free electrons in the conductor will be equal to n Al.

Hence, the total charge q = - n Ale

The time taken by free electrons to cross the conductor is

where we have substituted for t and q.

For a given conductor, I a Vd

A small value of drift velocity 10-5m/sec produces a large amount of current, as there are a large number of

free electrons in a conductor.

The drift velocity of the electrons Vd is (using E = V / l)

Also I = - neAVd

On substituting for Vd in the above expression we get,

or

From this, the resistance R can be identified as

where,

R : resistance of the conductor

m : mass of the electrons

l : length of the conductor

n : density of free electrons in the conductor

e : electronic charge

A : area of cross-section

t : relaxation time

From this, the relaxation time r for a metal can be estimated, using the observed values of r. For copper at

room temperature, r = 1.7 x 102 mW m. The number density of electrons is ~ 8.5 x 1022 m-3 (using the density

of copper). Substituting these, along with the known values of m and e, we get t = 2 x 10-7 s, which agrees

with values obtained by other methods.

Mobility

In metals, the mobile charge carriers are the electrons, in an ionized gas, they are electrons and positive

ions; in electrolytes, these are both positive and negative ions. In a semiconductor such as Ge or Si,

conduction is partly duer to electrons and partly due to holes which are sites of missing electrons. Holes act

as positive charges.

The mobility m is defined as the magnitude of the drift velocity per unit electric field, i.e.,

 

 

Mobility is positive for both electrons and holes.

The electrical conductivity of a superconductor can be expressed as

s = neme + pemh

Here, me, mh are electron and hole mobilities and n,p are electron and hole concentrations.

The S.I unit of mobility is m2 / Vs.

Mobilities of some materials, at room temperature, in cm2/vs

Material Electrons Holes

Diamond 1800 1200

Silicon 1350 480

Germanium 3600 1800

InSb 800 450

GaAs 8000 300

The resistivity of a metallic conductor nearly always increases with increasing temperature. As temperature

increases, the ions of the conductor vibrate with greater amplitude, making it more likely that a moving

electron will collide with an ion. This impedes the drift of electrons and hence the current. Over a small

temperature range, the resistivity of a metal can be represented by a linear relation

where ro is the resistivity at a reference temperature To and r (T) is the resistivity at temperature T. a is called

the temperature coefficient of resistivity and has dimensions of (oC)-1.

However, the temperature dependence of r at low temperatures is non-linear as shown in figure given

below.

Fig (a) - Resistivity rT of copper as a function of temperature T

In metallic alloys, the resistivity is very large, but has a weak temperature dependence, as seen in below

figure.

Fig(b) - Resistivity rT

of nichrome as a function of absolute temperature T

Alloys have a residual resistivity even at absolute zero, but a pure metal has a vanishingly small resistivity.

This can be used to check the purity of metals.

The resistivity of a semiconductor decreases rapidly with increasing temperature as shown in fig (c).

Fig (c) - Temperature dependence of resistivity for a typical semiconductor

This means that a is negative. The resistivity of an insulator too decreases exponentially with increase in

temperature.

These observations may be understood qualitatively using the equation for r.

Since m and e are constants,

In metals, the number of free electrons, n does not change with temperature. But, as temperature increases,

the atoms/ions vibrate with increasing amplitude. Therefore, the collisions of electrons with them become

more frequent, resulting in a decrease in t. This means an increase in r with increase in temperature.

In both insulators and semiconducotors, t remains almost constant, but the number of free charge carriers

increases with temperature. At any temperature T, the number of carriers is given by

n(T) = n0 exp (-Eg/kB T)

where Eg is the energy gap between the conduction and valence bonds. From this, we can get the

temperature dependence of r to be

r(t) = r0 exp (Eg/kB T)

In semiconductors, Eg ~ 1 eV, \ r is not very high.

In insulators, Eg >> 1 eV; \ r is very high.

Also, this last equation shows that for semiconductors and insulators, resistivity increases with decreasing

temperature.

Ohm's law is not a fundamental law of nature. There are a number of commonly used circuit elements which do not obey

this law. They have one or more of the following properties:

1. V depends on I non-linearly.

2. The relationship between V and I depends on the sign of V for the same absolute value of V.

3. The relation between V and I is non-unique, that is, for the same current I, there is more than one value of voltage V.

Some materials, including several metals and alloys, exhibit a phenomenon called superconductivity. As the temperature

decreases, the resistivity at first decreases smoothly like that of any metal. But then at a certain critical temperature T C, a

phase transition occurs and the resistivity drops suddenly to zero. And electric current established in a super conducting

ring continues indefinitely without the presence of any driving field. Superconductivity was discovered in 1911 by the

Dutch physicist Heike Kamerlingle Onnes.

Superconductors display the Meissner effect which is discussed below.

Meissner Effect

In 1933, Meissner and Ochsenfeld found that if a superconducting material is cooled to below its transition temperature, in

a magnetic field, then the lines of induction B are pushed out. This is shown in the figure below.

Meissner effect in a superconductor

The Meissner effect shows that a bulk superconductor behaves as if inside it, B is zero.

High Tc Superconductivity

This table shows that some materials, mainly oxides, have a fairly high critical temperature Tc. The 125K bulk super

conducting oxide was discovered in 1988. High Tc superconductors have promising commercial applications in thin film

devices, levitated vehicles and long distance power transmission.In MRI (magnetic resonance imaging) instruments, superconducting magnets made with these high Tc materials

are being used. These can be cooled with liquid nitrogen. Earlier, liquid helium was required which was much more expensive

RESISTORS IN SERIES AND PARALLEL

When resistors, can be connected in such a way that the same current flows in them, then they are said to be connected

in series. The resistors are said to be connected in parallel if the potential difference is the same across each resistor.

For any combination of resistors in a circuit, we can always find a single resistor that can replace the combination and

result in the same total current and potential difference.

For example, a string of light bulbs can be replaced by a single, chosen light bulb that can draw the same current and

have the same potential difference between its terminals as the original string of bulbs. The resistance of this single

resistor is called the equivalent resistance of the combination.

Resistances in Series

If the resistances are connected end-to-end, the same current flows through each resistance, as there is no alternative

path. Then

where I is the current, V is the potential difference of the battery and RS is the equivalent resistance of the combination.

Now,

V = V1+V2+V3

IRS = I1R1 + IR2 + IR3 Therefore,

RS = R1+ R2 + R3

Resistance in Parallel

If the resistance are in parallel, the potential difference across each is the same, but the current is not. Then,

I = I1 + I2 + I3

Since charge is not accumulated at a point,

where Rp is the equivalent resistance of the combination. Therefore,

For the special case of only two resistors in parallel, the expression for the equivalent resistance takes on a particularly

simple form, i.e.,

Next, consider the following two networks where the resistances are connected in series - parallel combinations.

The first network can be simplified by replacing the parallel combination of R2 and R3 with its equivalent resistance. This is

then in series with R1.

In the second network, the combination of R2 and R3 in series forms a simple parallel combination with R1.

But, not all networks can be reduced to simple series - parallel combinations, and special methods are required.

ELECTRICAL CIRCIUT AND KIRCHOFF RULE

In many electrical circuits, Ohm's law cannot be applied. This happens when there is more than one source of emf in the

circuit or when resistors are connected in a complicated manner. To solve such complex circuits, Gustav Robert Kirchhoff

developed two laws based on charge neutrality in a metal.

Here, we first discuss the internal resistance of electrical circuits and then go on to Kirchhoff's rules.

Internal Resistance

When current is drawn from a cell, ions move within the cell from one electrode to another. The resistance offered by the

electrodes and electrolytes to these, measure the internal resistance of the cell.The internal resistance of a cell depends

on the distance between the plates, the nature of the electrolytes, the concentration of electrolytes, the nature of the

electrodes and the area of the plates.

It is usual practice to represent internal resistance of a cell like a series resistor, external to the cell as shown.

Consider the circuit below.

Let e, r be the emf and internal resistance of a cell and R - the external resistance. A high resistance voltmeter V is

connected as shown.

When K is opened (i.e., open circuit) emf, the voltmeter reads the emf (e) of the cell as no current flows through the

circuit.

When K is closed (i.e., closed circuit), a current 'I' flows in the circuit. Hence, we have

'Ir' is the potential difference across the internal resistance r.

But, V = IR

Therefore, the external voltage V is less than the emf of the cell, e. It is as though an internal resistance r is in series with

the external resistance R, and this determines the current in the circuit for a given source of emf.

Also,

Kirchhoff's Rules

Consider the following two circuits. Neither can be solved by series-parallel combinations.

Many practical resistor networks cannot be reduced to simple, series-parallel combinations. The above circuit shows a DC

power supply with EMF E1 charging a battery with a smaller EMF E2 and feeding current to a light bulb with resistance R.

Here we cannot identify the resistances in series or in parallel. So, German physicist Gustow Robert Kirchoff developed a

technique. He introduced two terms. One is 'junction' and the other is 'loop'.

Before going on to Kirchoff's rules, we need to introduce two terms - junction and loop.

In the above circuits a, b, c, d are junctions but not e, f.

Some possible loops are acdba, acdefa, abdefa and abcdefa.

Kirchhoff's Junction Rule

The algebraic sum of the currents at a junction in a closed circuit is zero.

Therefore, I1 + I4 = I2 + I3 + I5

Hence, I1 + I4 - I2 - I3 - I5 = 0

or SI = 0

(Sum of currents entering a junction = Sum of currents leaving the junction)

This rule is based on the fact that charge cannot be accumulated at any point in a conductor in a steady situation.

Kirchhoff's Loop Rule

The algebraic sum of the potential differences in any loop including those associated with emfs and those of resistive

elements must be equal to zero.

This rule is based on energy conservation, i.e., the net change in the energy of a charge after completing the closed path

is zero. Otherwise, one can continuously gain energy by circulating charge in a particular direction.

Sign Convention in Applying Kirchhoff's Rules

The emf of a cell is positive when one moves in the direction of increasing potential (i.e., negative pole to positive pole)

through the cell and is negative when one moves from positive to negative.

The product of resistance and current, i.e., the IR term, in any arm of the circuit is taken negative if one moves in a closed

path, in the same direction of the assumed current; and positive if in the opposite direction.

Steps to solve circuits by Kirchhoff's laws:

Assume unknown currents in a given circuit and show their directions by arrows.

Choose any closed loop and find the algebraic sum of voltage drops plus the algebraic sum of the emfs in that

closed loop and equate it to zero.

Write equations for as many closed loops as the number of unknown quantities. Solve the equations to find the

unknown quantities.

If the value of assumed current is negative, it means that the actual direction of the current is opposite to that of

the assumed direction.

Voltmeter and Ammeter

These devices measure the voltage and current respectively in a circuit. The basic component of both is the moving coil

galvanometer which produces a deflection proportional to the electric current through it.

Ammeter

An ammeter is connected in series with the circuit element whose current is to be measured, so that there is only a

negligible change in the circuit resistance and hence circuit current.

Let the galvanometer resistance be G and the current for full-scale deflection be Ig. To measure larger currents, a suitable

low resistance S (called shunt) is connected in parallel with the galvanometer.

The value of S is chosen by the maximum current I that we want to measure. This means that though the circuit current is

I, only a current Ig should be through the galvanometer. The remaining current

I - Ig = Is should flow through the shunt. Equating potential differences across the shunt and galvanometer, we get

(I - Ig) S = Ig G

The resistance of the ammeter (i.e., shunted galvanometer) is

\ RA < S

So, the shunt not only extends the range of current (from Ig to I), it extends the range of current (from G to RA) of the

ammeter.

Voltmeter

A voltmeter is connected in parallel with the circuit element across which potential difference is to be measured. It should

have a very high resistance as not to alter the circuit resistance, and hence circuit current.

The galvanometer can measure voltages upto IGG. For larger potential differences, a suitable high resistance R (called

multiplier) is connected in series.

The value of R is chosen according to the maximum voltage V that we want to measure. But the galvanometer by itself

can only handle a voltage of IgG. The remaining potential difference (V - IgG) should be across the multiplier R. The

current through it is Ig. Therefore, equating voltage drops, we get

V = Ig G + Ig R

The resistance of the voltmeter (i.e., a galvanometer in series with a high resistance) is

RV = G + R

Since R is high, the multiplier increases the resistance of the voltmeter, and of course, extends the voltage range (from

IgG to V).

Wheatstone Bridge

This is used to measure an unknown resistance accurately. It consists of 4 resistors (2 fixed known resistances P and Q,

a known variable resistance R and the unknown resistance X) connected as shown in the figure.

Wheatstone's network

A source of emf is connected across one pair of opposite junctions (A and C), and a galvanometer G across the other

opposite pair (B and D). The key K1 is closed first and then K2. The value of R is varied till the galvanometer shows no

deflection, i.e., Ig = 0. Then, the bridge is said to be balanced.

The wheatstone bridge principle states that under balanced conditions, the products of the resistances in the opposite

arms are equal, i.e.,

We will show this using Kirchoff's rules.

Applying the Kirchhoff's law to loop 1, we have

-I1P - IgRg + (I - I1)R = 0 ...(1)

Similarly for loop 2, we have

- (I1-Ig)Q +(I - I1+ Ig)X +IgRg = 0 ...(2)

(where Rg is the resistance of the galvanometer)

In the balanced condition, putting Ig = 0, we have

-I1P + (I - I1)R = 0 …(1)

And -(I1)Q + (I - I1)X = 0 …(2)

Simplifying the two equations, we get

I1P = (I-I1)R …(1)

I1Q = (I-I1)X …(2)

Dividing the above two equations, we get

Resistor Q is called the standard arm of the bridge, and resistor P and R are called the ratio arms.

Metre Bridge

This is the simplest form of wheatstone bridge and is specially useful for comparing resistances more accurately. The

construction of the metre bridge is as shown in the below figure.

It consists of one metre resistance wire clamped between two metallic strips bent at right angles and it has two points for

connection. There are two gaps; in one of them a known resistance whose value is to be determined is connected. The

galvanometer is connected with the help of jockey across BD and the cells is connected across AC. After making

connections, the jockey is moved along the wire and the null point is obtained. The segment of length l 1 and (100-l1) form

two resistances of the wheatstone bridge, the other two reistances being R and S. The wire used is of uniform material

and cross-section. The resistance can be found with the help of the following relation

where s is the resistance per unit length of the wire and l1 is the length of the wire from one end where null point is

obtained. The bridge is most sensitive when null point is somewhere near the middle point of the wire. This is due to end

resistances.

End Correction

Sometimes at the end points of the wire, some length is found under the metallic strips and as a result, in addition of

length l1 or (100 - l1), some additional length should be added for accurate measurements. The resistance due to this

additional length is called end resistance. If the end resistance is small, it can be determined by first introducing known

resistances P and Q in the gap and obtaining the null point reading l1, then interchanging P and Q and obtaining the null

point reading l2. Let a and b be the lengths on the respective end under the metallic strips, then we have

Solving the equations (1) and (2) for a and b, we have

Hence the values of a, b can be calculated and suitably accounted for when accurate measurements are required.

Potentiometer

This instrument is identical to the meter bridge except that in this case, the resistance wire is of more than a meter length.

This enables greater accuracy. A standard cell of emf e1 maintains a constant current throughout the wire. As the wire is

of uniform material and cross section, it has uniform resistance per unit length. The potential gradient, i.e., r, depends

upon the current in the wire.

If an emf e1 is balanced against the length, say, l1 we have

Similarly, if another emf e2 is balanced against the length, say, l2, we have

From equations (1) and (2), we have

 

 

From the above figure, by means of a battery B and rheostat Rh, a steady current is passed through the potentiometer

wire AC. Two cells e1 and e2 whose emf's are to be compared are put in such a way that positive terminals are connected

to A and negative terminal to the galvanometer through a two-way plug key k.

First the cell e1 is connected by connecting 1 and 3 points of key K2 and by moving the jockey K on the potentiometer

wire, the no deflection point is obtained. Let the reading be l1, then

where r is the potential gradient and l1 is the length CN. After this, the points 2 and 3 of the key K2 are connected i.e., the

cell of emf e2 is put into the circuit and again the no deflection point on the wire is obtained. Let this reading be l2. Then

e2 = rl2

Different sets of observations are taken by varying the variable resistance Rk and then mean value of ratio is computed.

SUMMARY

Current through a given area of a conductor is the net charge passing per unit time through the area.

To maintain a steady current, we must have a closed circuit in which an external agency moves electric charge

from lower to higher potential energy. The work done per unit charge by the source in taking the charge from lower to

higher potential energy (i.e., from one terminal of the source to the other) is called the electromotive force, or emf, of

the source. Note that the emf is not a force; it is the voltage difference between the two terminals of a source in open

circuit.

Ohm's law; the electric current I flowing through a substance is proportional to the voltage V across its ends.

i.e., V I or V = RI. where R is called the resistance of the substance. The unit of resistance is ohm: 1W = 1VA-1.

The resistance R of a conductor depends on its length l and constant cross-sectional area A through the

relation.

where r, called resistivity is a property of the material and depends on temperature and pressure.

Electrical resistivity of substances varies over a very wide range. Metals have low resistivity, in the range of 10 -

8Wm to 10-6Wm. Insulators like glass and rubber have 1022 to 1024 times greater resistivity. Semiconductors like Si

and Ge lie roughly in the middle range of resistivity on a logarithmic scale.

In most substances, the carriers or current are electrons; in some cases e.g., ionic crystals and electrolytic

liquids, positive and negative ions carry the electric current.

Current density j gives the amount of charge flowing per second per unit area normal to the flow.

j = nqv

where n is the number density (number per unit volume) of charge carriers each of charge q, and v is the drift velocity of

the charge carriers. For electrons q = -e. If j is normal to a cross-sectional area A and is constant over the area, the

magnitude of the current I through the area is (nev A).

Using E = V/l, I = nev A and ohm's law, one obtains.

The proportionality between the force eE on the electrons in a metal due to the external field E and the drift velocity v d (not

acceleration) can be understood, if we assume that the electrons suffer collisions with ions in the metal, which deflect

them randomly. If such collisions occur on an average at a time interval t,

vd = at = eEt/m

where a is the acceleration of the electron. This gives

In the temperature range in which resistivity increases linearly with temperature, the temperature coefficient of

resistivity a is defined as the fractional increase in resistivity per unit increase in temperature.

Ohm's law is obeyed by many substances, but it is not a fundamental law of nature. It fails if

(a) V depends on I non-linearly.

(b) The relation between V and I depends on the sign of V for the same absolute value of V.

(c) The relation between V and I is non-unique.

An example of (a) is when increases with I (even if temperature is kept fixed). A rectifier combines features

(a) and (b). A thyristor shows all the features (a), (b) and (c).

When a source of emf e is connected to an external resistance R, the voltage Vext across R is given by

where r is the internal resistance of the source.

(a) Total resistance R of n resistors connected in series is given by

R = R1 + R2 + …Rn

(b) Total resistance R of n resistors connected in parallel is given by

 

 

Kirchhoff's Rule

(a) First Rule (Junction Rule): At any junction of circuit elements, the sum of currents entering the junction must equal the

sum of currents leaving it.

(b) Second Rule (Loop Rule): The algebraic sum of changes in potential around any closed loop must be zero.

A voltmeter consists of a galvanometer (or resistance RG) in series with a high resistance R. It is put in parallel

to the circuit element across which the voltage is to be measured. Because of its high (R + R @ R). It draws a very

small current and thus does not disturb the circuit. If the full scale deflection of the galvanometer occurs for a current

Io and the voltmeter is to have range Vo, we have

An ammeter consists of a galvanometer (or resistance RG) and low resistance R in parallel. The effective

resistance of the ammeter is

Because of its very low resistance, the ammeter placed in series in a circuit does not materially change the current in the

circuit to be measured. If the full-scale deflection of the galvanometer occurs for current I o and the ammeter is to have a

range Imax, we have

The potentiometer is a device to compare potentials. Since the method involves a condition of no current flow,

the device can be used to compare emfs of two sources.

The Wheatstone bridge is an arrangement of four resistances - P, Q, R, S as shown in the text. The null-point

condition is given by

 

 

using which the value of one resistance can be determined, knowing the other three resistances.

PROBLEMS AND SOLUTIONS

01.

In the case of hydrogen atom, an electron moves in an orbit of radius 5x10 -11 m with a speed of 2.2 x 106 ms-1. Calculate

the equivalent current. Given: charge on an electron = 1.6 x 10-19C.

Suggested solution:

Radius of the orbit, r = 5 x 10-11m

Circumference = 2pr

Speed of electron,

Number of revolutions in 1 second,

Charge flowing in one second, q = nr

Current,

02.

How many electrons flow through the filament of a 120 V, 60 W electric lamp in one second? Given: Electric power is the

product of voltage and current.

Suggested solution:

Now,

or

03.

What is the number of free electrons in a piece of silver of cross-section 1.0 x 10-4 m2 and length 1m? Atomic weight of

silver = 108, density of silver = 105 x 102 kg m-3. Assume that there is one free electron per atom.

Suggested solution:

Area, A = 1.0 x 10-4 m2

Length, l = 1 m

Atomic weight = 108

Density, d = 105 x 102 kg m-3

Volume of given piece = A x l = 1.0 x 10-4 m2 x 1m = 10-4 m3

Mass = Volume x density = 10-4 m3 x 105 x 102 kg m-3 = 1.05 kg

Number of atoms in 108 kg silver = 6.023 x 1026

Since there is only free electron per atom, therefore the number of free electrons is 5.856 x 1024