Current Electricity

CURRENT ELCTRICITY Topics: - Electric Potential - Potential difference - Capacitors - Ohm’s law - Electrical power and energy - Kirchhoff’s law Electric Potential Electric potential (V) at a point a distance r from a positive charge Q is the work done in moving a unit positive charge from infinite distance to the point. Its mathematical expression is

V=

1 Q 4π Eo r

If r is infinitely large, V goes to zero Potential Difference The potential difference between two points in an electric circuit is defined as the amount of work done in moving a unit charge from one point to the other point. That is potential difference =

V=

W Q

where

Work done Quantity of ch arg e moved

W = work done Q = quantity of charged moved

Unit of V

1 volt =

1 joule coulomb

1V =

1J ⇒ V = JC −1 1C

Thus potential difference is measured by means of an instrument called voltmeter. Capacitors “Capacitor is a device which is used to store large quantity of charge.” The combinations of the conductors of any shape held near to each other which carrying equal and opposite charges. These conductors are called plates of the capacitor. Between the two plates of capacitor either air or any insulating medium (wax, oil, glass etc) is kept. These substances are called dielectric. Capacity of capacitor or Capacitance =

Magnitudeof ch arg eof either plate Magnitudeof Potential Difference C=

Q V1 − V2

Parallel plate capacitor Fig A shows the parallel plate capacitor. Two plane plates each of area A, are separated by a small distance d. The capacitance of this capacitor is

C=

Eo Er A or d

C=

Eo KA … (1) d

If the medium present between the plates is vacuum then Er = 1 or K = 1

C=

Eo A d

… (2)

Fig A. Parallel Plate Capacitor So that a dielectric filled parallel plate capacitor has a capacitance K times larger than the same capacitors with vacuum between its plates. ur Unit of C

S.I

C=

E0 Er A farad d

When A is taken in

CGS

C=

Er A 4π d

cm 2 and d in meter

stat farad

Where A is taken in cm2 and d in cm. Combination of Capacitors In most of the experiments, we required a definite value of capacitors which can be obtained by mutual combination of capacitors. These are 1. Series combination 2. Parallel combination

Series Combination

q = q1 = q2 = q3 V = V1 + V2 + V3 1 1 1 1 = + + Ceq C1 C2 C3

Parallel Combination

q = q1 + q2 + q3 V = V1 = V2 = V3 Ceq = C1 + C2 + C3 Electric Current The electric current is a flow of electric charges C called electrons in a conductor such as a metal wire. This electric charges flow due to potential difference between the end of the wire. If a charge Q coulombs flow through a conductor in time t second. Then magnitude of the electric current is given by

I=

Q t

Here q is in coulomb, t is in seconds and I is in amperes (1 A= 1 C/s) OHM’s Law At constant temperature the current flowing through a conductor is directly proportional to the potential difference across its ends.

I αV or

Vα I

V =Rα I Here R is a constant called ‘resistance’ of the conductor. Its value depends on the nature, length area of cross-section of the conductor. Its unit is the Ohm for which the symbol Ω (greek omega) is used 1 Ω= 1

V A

Resistivity The resistance R of a wire of length l and cross-section A is

R=ρ

l A

Where ρ is a constant called the resistivity. The resistivity is a characteristics of the material with which the wire is made. Effect of temperature on resistance Resistance of all conductors is found to increase with increase in temperature of the conductor. If a conductor has resistance R1 at t10C which becomes R2 at t20C ( t2 0C > t10C ) then increase in resistance ( R2 − R1 ) is found to be depend upon 1. Original resistance R1

( R2 − R1 ) α R1 2. Increase in temperature

( R2 − R1 ) α (t2 − t1 )

( R2 − R1 ) α R1 (t2 − t1 ) Combining

or ( R2 − R1 ) = α R1 (t2 − t1 )

Where α is constant of proportionality. It is called temperature coefficient of the material of conductor.

α=

( R2 − R1 ) R1 (t2 − t1 )

Unit of

α =

Ohm = OC −1orK −1 Ohm × temp

Combination of Resistances To get the required amount of current in the circuit it is necessary to combine two or more resistance. The resistance can be combined in two ways

1. Series Combination: If we want to increase the total resistance, then the individual resistances are connected in series

Then combine resistance is given by

R = R1 + R2 2. Parallel combination: It is used to decrease the total resistance

According to the law of combination of resistance in parallel: The reciprocal of the combined resistance of a number of resistances connected in parallel is equal to the sum of the reciprocal of all the individual resistances

1 1 1 = + R R1 R2 The equivalent resistance in a parallel is always less than the smallest of the individual resistances. Electrical Power

Electric work The electric work (in joules) required to transfer a charge q (in coulombs) through a potential difference V (in volts is given by)

W = qV Electrical Power Electric power (in watts) is the electrical work done (in joules) per unit time (in sec)

That is power =

P

or

=

W T

P=

qV T

because

W ork D one T im e ta k e n

q = I . This can be written as T

P = IV Where I = is in amperes. According to ohm’s law V

= IR . It becomes

P = I ( IR ) P = I 2R V2 orP = R Then the resistance of high power devices is smaller than the low power ones.

Electric Energy The electrical energy consumed by an electrical appliance depends on two things (1) power rating of the appliance and (2) time for which the appliance is used. In the mathematical form Electrical energy = Power x Time

E = P×t Kirchhoff’s law To study complex circuit, German Physicist Gurtav Robert Kirchhoff gave two laws are known as Kirchhoff’s law. 1. Kirchhoff’s current law or Junction law: In a network of conductors, the algebraic sum of all currents meeting at any junction of an circuit is always zero i.e.

∑I = 0 Current reaching towards the junction is taken as positive and current leaving the junction is taken as negative.

I1 + I 2 − I 3 − I 4 = 0

2. Kirchhoff’s Voltate law or loop rule The net potential drop in a closed electronic network equals the sum of the products of current and corresponding resistance.

∑R = ∑E (i) If we traverse in the circular direction of current in a mesh, then the product of current and corresponding resistance is taken as positive and opposite to conventional current will be negative. (ii) If we travel from the negative to positive electrodes of the cell through the electrolyte, then EMF is taken as positive otherwise negative. ______________________________________