## 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.

^{2}v

^{-1}s

^{- 1}.

## Relation Between Current And Drift Velocity

_{d}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 = I^{2}R =(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 × 10^{6} 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 R_{s} = R_{1} + R2 + R_{3}

• For parallel combination net resistance is (1/R_{P})=(1/R_{1})+(1/R_{2})+(1/R_{3})

• 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 R_{t} = R_{0} [1 + αt]

where α is the temperature coefficient of resistance and R_{0} 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

• 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

_{s}= ε

_{1}+ ε

_{2}and r

_{s}= r

_{1}+ r

_{2}

• For parallel combination of cells, ε

_{p}=(ε

_{1}r

_{2}+ε

_{2}r

_{1}/r

_{1}+r

_{2}) and r

_{p}=(r

_{1}r

_{2}r

_{1}+r

_{2})

## 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.

∴ (R_{1}/R_{2})=(R_{3}/R_{4})