Chapter : 3

What Are Current Electricity ?

Electric Current

The rate of flow of electric charge through a conductor is called electric current.

• Elecrtric current, I =(q/t)=(Ne/t)

where q is the electric charge and N is the number of free electrons passing through a cross-section of a conductor in time t.

• If electric current flowing through a conductor is not steady, then I =(dq/dt)

• S.I. unit of electric current is ‘ampere’ which is denoted as ‘A’

Flow Of Electric Charges In A Metallic Conductor

• In solid conductors, free electrons move randomly in different directions nullifying their net effect and hence preventing any current flow.

• A steady electric current is established in the conductor with the application of constant electric field across it and this field is provided by cells or batteries.

Drift Velocity

Drift velocity of electrons,

$$\text{V}_\text{d}=\frac{-\text{e}\vec{\text{E}}}{\text{m}}\text{τ}$$

where e is the charge on electron, m is the mass,

$$\vec{\text{E}}$$

is the electric field applied and τ is the time of relaxation.

• Negative sign shows that drift velocity of electrons is in a direction opposite to the direction of applied electric field.

Mobility

Mobility is defined as the magnitude of drift velocity of charge carrier per unit electric field. It is given as,

$$\mu=\frac{|\text{V}_\text{d}|}{\text{E}}=\frac{\text{qEτ}/\text{m}}{\text{E}}=\frac{\text{qτ}}{\text{m}}$$

where q, τ and m are charge, relaxation time and mass of a charge carrier respectively.

• SI unit of mobility is m2v-1s- 1.

Relation Between Current And Drift Velocity

Electric current and drift velocity are related as I = neAvd where n is the number density of electrons, A is the area of cross-section of the conductor.

Ohm’s Law

According to Ohm’s law, the potential difference applied across the ends of a conductor is directly proportional to the current.

V ∝ I or V = IR

where R is the resistance of the conductor.

• Another form of Ohm’s law is,

$$\vec{\text{J}}=\sigma \vec{\text{E}}$$

Electrical Resistance

• The opposition offered by the conductor to the flow of electric current through it, is called its resistance.

• Resistance is measured in `Ohm’ and is denoted by ‘Ω’.

Vi Characteristics (Linear And Non-linear)

Under constant physical conditions, VI-graph of such substances is a straight line and resistance of conductor can be obtained using the slope of VI-graph.

• Ohm’s law is valid for good conductors. Semiconductor does not show linear behaviour between V and I.

R= (ΔV/ΔI)=(1/tanθ)

Electrical Energy And Power

• Electric power =(Electric work done/Time taken)

• P = VI = I2R =(V 2/R)

• Electrical energy = Electric power × time E = P × t

• SI unit of power is watt (W)

• The commercial unit of electric energy is kilowatt-hour (kWh),

1 kWh = 1000Wh = 3.6 × 106 J = one unit of electricity consumed

Electrical Resistivity And Conductivity

• Resistance of a conductor is directly proportional to its length l and inversely porportional to its cross-sectional area A i.e., R ∝(l/A) or R=p(l/A)

where p is a constant of material of the conductor which is known as its ‘resistivity’ or ‘specific resistance’.

• The reciprocal of resistivity is know as conductivity or specific conductance. σ =(1/p)

• Resistivity of a conductor is measured in Ω - m

• The SI unit of conductivity is Ω-1 m-1 or Sm-1 or mho m-1

Series And Parallel Combination Of Resistors

• For series combination, net resistance is Rs = R1 + R2 + R3
• For parallel combination net resistance is (1/RP)=(1/R1)+(1/R2)+(1/R3)

• For series combination of resistors, net resistance is more than the largest value of any resistance in the group.

• For parallel combination of resistors, net resistance is less than the smallest value of resistance in the group.

Temperature Dependence Of Resistance

• Resistance of a conductor at temperature t°C is Rt = R0 [1 + αt] where α is the temperature coefficient of resistance and R0 is the at 0°C.

• For metal α is positive, i.e., resistance increases with rise in temperature.

• For insulators and semiconductors α is negative i.e., resistance decreases with rise in temperature.

Internal Resistance Of A Cell

internalresistance

• Internal resistance of a cell, r =(ε-IR/I) or r=R((ε/V)-1)

where ε is the emf of the cell, and R is the external resistance.

Potential Difference And Emf Of A Cell

• Electromotive force or emf of a cell is defined as the potential difference between two terminals of a cell in an open circuit i.e. when no current flows through the cell.

• Terminal potential difference of a cell is defined as the potential difference between terminals of a cell in a closed circuit i.e., when some current is drawn from the cell.

V = ε – Ir

• The SI unit of emf is joule/coulomb or volt (V).

Combination Of Cells In Series And In Parallel

• For series combination of cells, εs = ε1 + ε2 and rs = r1 + r2
• For parallel combination of cells, εp =(ε1r22r1/r1+r2) and rp=(r1r2/r1+r2)

Kirchhoff’s Laws And Simple Applications

Kirchhoff’s first law

• It states that the algebraic sum of the currents at a junction is zero. It is also known as Kirchhoff’s junction law or current law.

• Kirchhoff’s first law supports law of conservation of charge.

Kirchhoff’s second law

• It states that in a closed loop, the algebraic sum of the emf’s is equal to the algebraic sum of products of the resistance and the respective currents flowing through them, Σε = Σ IR

• Kirchhoff’s second law supports law of conservation of energy.

Wheatstone Bridge

For a balanced Wheatstone bridge, current through the galvanometer is zero.

∴  (R1/R2)=(R3/R4)