Pre-requistie

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Pre-requistie

P ELECTRIC CHARGE

1) Electric Charge is the fundamental property of a matter that exhibit electrostatic attraction or repulsion over other matter.

2) We know that atom consists of electrons, protons and neutrons. Each electron has negative charge and proton has positive charge. A neutron carries no charge and is therefore neutral.

3) Every atom consists of equal number of electrons and protons and hence the atom is electrically neutral.

4) If an atom loses an electron it is left with an overall positive charge and such a charged atom is called positive ion. If an electron is added to an atom then it attains negative charge and such a charged atom is called negative ion.

UNIT OF CHARGE 1) The SI unit of charge is coulomb (C). One coulomb is the amount of charge that is transferred through the cross section of a wire in 1second when there is a current of 1 Ampere in the wire.

2) Also, the charge of one electron is 1.602 x 10-19, so we can say that, one coulomb is the amount of charge on i.e.

1 electrons.

1.602 1019

One coulomb = charge on 6.24 x 1018 electrons

ELECTRICAL CURRENT 1) Electrical current is a measure of the amount of electrical charge transferred per unit time. It represents the flow of electrons through a conductive material. i.e.

I=

Q t

where I = Average current flow (Amp) Q = Total charge Transferred (Coulomb) t = Time required to transfer the charge (sec)

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VOLTAGE 1) It is defined as the work done per unit charge. Let ‘W’ joules of energy be required to move a positive charge of ‘Q’ coulombs from one point to another in a circuit, then we say that voltage exits between two points. i.e.

E =V =

W Q

POWER 1) Power is defined as the rate of doing work or rate of charge of energy. i.e.

2) But I =

P= Q t



Energy W VQ = = Time t t

P=VI

3) According to the Ohms Law, V = I R,

V2 2 P=VI= =I R R



….. (1)

4) Power is measured in watt (W). The higher units of power are kilo watts (kW), mega watts (MW). Another most widely used unit of power is ‘Horse Power’. The relation between HP and Watt is, 1 HP = 746 watts Energy 1) Energy is defined as the capacity to do the work. It is measured in joules (J).

E=Pxt 2) From equation (1) we have,

E=VIt =

V2 t = I2 R t R

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Resistance 1) Resistance is the property of a substance due to which it opposes the flow of current through it.

2) Certain Substances offer very little opposition to the flow of current and are called as conductors e.g. metals, acids and salt solutions, Certain substances offer very high resistance to the flow of current and are as called insulators e.g. mica, glass, rubber, Bakelite.

3) The unit of resistance is ohm (  ). A conductor is said to have a resistance of one ohm if a potential difference of one volt across its terminals causes current of one ampere to flow through it.

4) The resistance of a conductor, a) is directly proportional to its Length. b) is directly proportional to the Area of Cross Section. c) depends on the nature of the material. d) also depends on the temperature of the conductor.

Hence,

R=ρ

l A

…. (2)

Where l = Length of the conductor A = Area of cross section

ρ = Specific Resistance or Resistivity 5) Specific Resistance or Resistivity: The specific resistance or resistivity of a material is the resistance offered by unit length of the material of unit cross section. If the length is in meter and the cross section in square meter, then the resistivity is expressed in ohm-meter (  -m).

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Conductance 1) Conductance is the property of a substance due to which it assists the flow of current through it.

2) Mathematically, conductance is defined as the reciprocal of resistance i.e.

(1/R). It is denoted by G and measured in mho or Siemens.

1  G= R 1 [From equation 2]  G= l ρ A 1A  G= ρ l 3) The quantity 1/p is called as conductivity denoted by σ .

1 (Siemens/m) or (mho/m)  σ= ρ EFFECT OF TEMPERATURE ON RESISTANCE 1) The resistance of all pure metals increases with increase of temperature almost linearly over a limited temperature range.

2) In case of certain alloys, increase in resistance with increase of temperature is not appreciable. These alloys show practically no change of resistance for a considerable variable of temperature.

3) In case of electrolytes, insulators and partial conductors such as carbon, resistance of the material decreases with increase of temperature.

4) The change in resistance of a material with rise in temperature can be expressed b means of temperature coefficient of resistance.

5) Consider a conductor having resistance Ro at 0oC and Rt at toC. Then in the normal range of temperatures, the increase in resistance i.e. (Rt – R0) a) is directly proportional to the initial resistance. b) is directly proportional to the rise in temperature. c) also depends upon the nature of the material.

Hence, (Rt – R0) = αR 0 t Where, α = Temperature coefficient of Resistance at 0oC. Its value depends upon the nature of the material and temperature. i) Thus, the resistance of a conductor at toC is Rt = R0 (1 + α t)

…… (3)

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EFFECT OF TEMPERATURE ON TEMPERATURE COEFFICIENT 1) Suppose that a conductor is heated from one initial temperature t1oC to a final t2oC. Let R1 and R2 be the resistances of a material at t1oC and t2oC respectively and α 1 and α 2 be the corresponding temperature coefficients. Then, R2 = R1 [1 + α 1 (t2 – t1)]

……. (4)

2) From equation (3) we can write, R 2 = R 0 (1+α0 t 2 ) and R1 = R 0 (1+α0 t1 ) R 2 1+α0 t 2 = R1 1+α0 t1



1+α0 t 2  R 2 = R1    1+α0 t1 



…… (5)

 Fromequation (4)and (5) 1+α0 t 2  R1 1+α1 (t 2 -t1 ) = R1    1+α0 t1  

1+α0 t 2  1+α1 (t 2 -t1 ) =    1+α0 t1 



1+α0 t 2  α1 (t 2 -t1 ) =   -1 1+α t 0 1 



α1 (t 2 -t1 ) =



α1 =

α0 (t 2 -t1 ) 1+α0 t1

α0 1+α0 t1

Similarly, we can prove that, α 2 =

α0 1+α 0 t 2

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OHM’S LAW Statement The potential Difference across any two points on a conductor is directly proportional to the current flowing through it, provided the physical conditions i.e. material length, cross sectional area and temperature of the conductor remain constant.

Mathematically,

Potential Difference  Current

1) For D.C. Circuits the above law can be expressed as, V I

or

V = R.I

Where R = Resistance between two points of the conductor Unit: Ohms (  ) 2) For A.C. Circuits the above law can be expressed as, v i

or

v=Zi

Where Z = Impedance of circuit.

Unit: Ohms (  ) Where Z =

R2  X 2

R = Net Resistance and X = Net Reactance

Limitations 1) Ohm’s law does not apply to non-metallic conductors.

2) Ohm’s

law

also

does

not

apply

to

non-linear

devices

such

as

semiconductor components.

3) Ohm’s law is true for metal conductors at constant temperature. If the temperature changes, the law is not applicable.

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