CURRENT ELECTRICITY

CH 2(A) ELECTRIC CURRENT AND RESISTANCE

#) Current Carriers. The charged particles whose flow in a definite direction constitutes the

electric current are called current carriers. e.g. electrons in conductors, ions in electrolyte,

electrons and holes in semiconductor.

#) Electromotive force of a cell is defined as the maximum potential difference between the

two electrodes of a cell when the cell is in the open circuit. E.M.F of a cell depends upon

nature of electrodes, nature and concentration of electrolyte used in the cell and its

temperature.

#) Electric Current. The flow of charge in a definite direction constitutes the electric current.

S.I unit of current is ampere. The arrow head marked in circuit represents the direction of

conventional current I.e. direction of flow of positive charge, whereas the direction of flow

of electrons gives the direction of electronic current which is opposite to that of

conventional current. Current is a scalar quantity.

#) Drift Velocity. It is defined as the average velocity with which free electrons get drifted

towards the positive end of the conductor under the influence of an external electric field.

#) Relation between current and drift velocity mobility.

1= nAe v d = A ne µ e E

Where n is the electron density or no. Of electrons per unit volume of the conductor and A is

the area of cross-section of the conductor. The small value of the drift velocity ( - 10-5 ms-1 )

produces a large amount of current due to presence of large number of free electrons in a

conductor (- 1029 m-3). The propagation of current is at the speed of light.

#) Ohm's law. It states that the current (I) flowing through a conductor is directly

proportional to the potential difference ( V ) across the ends of the conductor, provided

physical conditions of the conductor such as temperature, mechanical strain etc. are kept

constant I.e. V * 1 or V = IR

Where R is known as resistance of the conductor, which depends upon the nature and

dimensions of the conductor. The S.I. unit of R is ohm.

#) Resistance of a conductor. It is the obstruction posed by the conductor to the flow of

current through it. Resistance of a conductor is due to the collisions of free electrons with

the ions or atoms of the conductor while drifting towards the positive end of the conductor.

#) Specific resistance or electrical resistivity of the material of a conductor is defined as the

resistance of unit length and unit area of cross, section of the conductor. The S.I unit of

resistivity is m. Resistivity of a conductor depends upon the nature of the conductor but is

independent of the length or area of cross section of the conductor.

#) Current density at a point is defined as the amount of current flowing per unit area of

cross-section of the Conductor, provided the area is held in a direction normal to the

current.

The S.I. unit of current density is Am -2

#) Electrical conductivity of a conductor is the inverse of its resistivity. The S.I unit of ó .

#) Effect of temperature on resistance. The resistance of a metal conductor at a

temperature t 0 C is given by R t = R 0 (1 + a t )

Where R o is the resistance of a conductor at 0o C and a is the temperature co-efficient of

resistance.

For metals a is positive I.e. resistance increases with rise in temperature.

For semi conductor and insulators a is negative I.e. resistance decreases with rise in

temperature.

For alloys like manganin, eureka and constantan, the value of a is very small as compared to

that of conductors. That is why these alloys are used in making standard resistances.

#) Non-ohmic conductors. Those conductors which do not obey Ohm's law are called non-

ohmic conductors e.g. vacuum tube, liquid electrolyte etc.

#) Super-conductors. Those materials which offer least resistance to the flow of current

through them are called super-conductors. Examples: mercury at temp. 4.2 K, lead at 7.25 K

and niobium at temperature 9.2 K become super-conductors.

The conductivity of superconductor is called superconductivity.

#) Color code for carbon resistors. The number attached from 0 to 9 to the various colors

can be recollected by the sentence B.B. ROY Great Britain Very Good Wife.

Black -0, Brown-1, Red-2, Orange-3, Yellow-4, Green-5, Blue-6, Violet-7, Grey-8, White-9. The

strip of gold, silver and no color shows the accuracy of 5%, 10% and 20% of the given carbon

resistor.

#) Resistance in series. The total resistance (R s ) is given by. R s = R 1 + R2 +R3 + ......

#) Internal resistance of a cell is defined as the resistance offered by the electrolyte and

electrodes of a cell when electric current flows through it. Internal resistance of a cell

depends upon: (I) distance between the electrodes, (ii) the nature of electrodes (iii) nature

of electrolyte and (iv) area of the electrodes immersed in the electrolyte.

#) Terminal potential difference of a cell is defined as the potential difference between the

two electrodes of a cell in a closed circuit. Terminal potential difference of a cell decreases if

the current drawn from the cell increases. Terminal potential difference of a cell ( V ) is less

than the e.m.f. of a cell by an amount equal to potential drop across the internal resistance

of the cell.

Where R is the external resistance in the circuit and r is the internal resistance of a cell.

#) Ch 2 (B) ELECTRIC MEASUREMENT

#) Kirchhoff's Laws.

First law: The algebraic sum of the current meeting at a junction is zero. The current

reaching a function if taken positive then the current leaving the junction is taken negative.

This law supports the concept that moving charges are not accumulated at a junction.

Second law: In a closed loop, the algebraic sum of all the potential difference is zero.

While traversing a closed loop. If negative pole of the cell is encountered first then its emf is

-ve , otherwise +ve. The product of resistance and current in an arm of the circuit is taken

positive if the direction of current in that arm is in the same sense as one moves in a closed

loop and is taken negative if the direction of current in that arm is opposite to the sense as

one moves in the closed loop.

#) Wheatstone bridge Principle: it states that if four resistances P,Q,R,S are arranged to

form a bridge as shown in Fig . 2.(b). 3 ,on pressing battery key K1 first and then

galvanometer key K2 , if the galvanometer shows no deflection, then the bridge is balanced.

#) Principle of potentiometer. It is based on the fact that the fakk of potential across any

portion of the wire is directly proportional to the length of that portion provides the wire is

of uniform area of cross section and a constant current is flowing.

CH 2 (C) HEATING EFFECT OF CURRENT

#) Joule's law of heating. It states that the amount of heat produced in a conductor is

directly proportional to the:

(I) square of the current flowing through the conductor, (ii) resistance of the conductor and

(iii) Time for which the current is passed.

#) Electric power. It is defined as the rate at which work is done in maintaining the current in

electric circuit.

Electric power, P = VI = 12 R = V2 /R watt or joule / second

#) Electric energy. The electric energy consumed in a circuit is defined as the total work done

in maintaining the current in an electric circuit for a given time.

Electric energy = VIt = P t = 12 Rt = v2 t / R

S.I unit of electric energy is joule (denoted by J )

Where 1 joule = 1 watt * 1 second = 1 volt * 1 ampere * 1 second

Commercial unit of electric energy is kilowatt hour ( k Wh ) where 1kWh = 1000 Wh = 3.6 *

106 J.