# Current Electricity

Electric Current (I)

The rate of flow of charge through any cross-section of a wire is called electric current flowing through it.

Electric current (I) = q / t. Its SI unit is ampere (A).

The conventional direction of electric current is the direction of motion of positive charge.

The current is the same for all cross-sections of a conductor of non-uniform cross-section. Similar to the water flow, charge flows faster where the conductor is smaller in cross-section and slower where the conductor is larger in cross-section, so that charge rate remains unchanged.

If a charge q revolves in a circle with frequency f, the equivalent current,

i = qf

(In a metallic conductor current flows due to motion of free electrons while in electrolytes and ionized gases current flows due to electrons and positive ions.)

Types of Electric Current

According to its magnitude and direction electric current is of two types

(i) Direct Current (DC) Its magnitude and direction do not change with time. A ceil, battery or DC dynamo are the sources of direct current.

(ii) Alternating Current (AC) An electric current whose magnitude changes continuously and changes its direction periodically is called alternating current. AC dynamo is source of alternating current.

Current Density

The electric current flowing per unit area of cross-section of conductor is called current density.

Current density (J) = I / A

Its S1 unit is ampere metre-2 and dimensional formula is [AT-2].

It is a vector quantity and its direction is in the direction of motion positive charge or in the direction of flow of current.

Thermal Velocity of Free Electrons

Free electrons in a metal move randomly with a very high speed of the order of 105 ms-1. This speed is called thermal velocity of free electron.

Average thermal velocity of free electrons in any direction remains zero.

Drift Velocity of Free Electrons

When a potential difference is applied across the ends of a conductor, the free electrons in it move with an average velocity opposite to direction of electric field. which is called drift velocity of free electrons.

Drift velocity vd = eEτ / m = eVτ / ml

where, τ = relaxation time, e = charge on electron,

E = electric field intensity, 1 = length of the conductor,

V = potential difference across the ends of the conductor

m = mass of electron.

Relation between electric current and drift velocity is given by

vd = I / An e

Mobility

The drift velocity of electron per unit electric field applied is mobility of electron.

Mobility of electron (μ) = vd / E

Its SI unit is m2s-1V-1 and its dimensional formula is [M-1T2A].

Ohm’s Law

If physical conditions of a conductor such as temperature remains unchanged, then the electric current (I) flowing through the conductor is directly proportional to the potential difference (V) applied across its ends.

I ∝ V

or V = IR

where R is the electrical resistance of the conductor and R = Ane2 τ / ml.

Electrical Resistance

The obstruction offered by any conductor in the path of flow of current is called its electrical resistance.

Electrical resistance, R = V / I

Its SI unit is ohm (Ω) and its dimensional formula is [ML2T-3A-2].

Electrical resistance of a conductor R = ρl / A

where, l = length of the conductor, A = cross-section area and

ρ = resistivity of the material of the conductor.

Resistivity

Resistivity of a material of a conductor is given by

ρ = m / n2 τ

where, n = number of free electrons per unit volume.

Resistivity of a material depend on temperature and nature of the material.

It is independent of dimensions of the conductor, i.e., length, area of cross-section etc.

Resistivity of metals increases with increase in temperature as

ρt = ρo (1 + αt)

where ρo and ρt are resistivity of metals at O°C and t°C and α temperature coefficient of resistivity of the material.

For metals α is positive, for some alloys like nichrome, manganin and constantan, α is positive but very low.

For semiconductors and insulators. α is negative.

Resistivity is low for metals, more for semiconductors and very high alloys like nichrome, constantan etc.

(In magnetic field the resistivity of metals increases. But resistivity of ferromagnetic materials such as iron, nickel, cobalt etc decreases in magnetic field.)

Electrical Conductivity

The reciprocal of resistivity is called electrical conductivity.

Electrical conductivity (σ) = 1 / ρ = 1 / RA = ne2 τ / m

Its SI units is ohm-1 m-1 or mho m-1 or siemen m-1.

Relation between current density (J) and electrical conductivity (σ) is given by

J = σ E

where, E = electric field intensity.

Ohmic Conductors

Those conductors which obey Ohm’s law, are called ohmic conductors e.g., all metallic conductors are ohmic conductor.

For ohmic conductors V – I graph is a straight line.

Non-ohmic Conductors

Those conductors which do not obey Ohm’s law, are called non-ohmic conductors. e.g., diode valve, triode valve, transistor , vacuum tubes etc.

For non-ohmic conductors V – I graph is not a straight line.

Superconductors

When few metals are cooled, then below a certain critical temperature their electrical resistance suddenly becomes zero. In this state, these substances are called superconductors and this phenomena is called superconductivity.

Mercury become superconductor at 4.2 K, lead at 7.25 K and niobium at 9.2 K

Colour Coding of Carbon Resistors

The resistance of a carbon resistor can be calculated by the code given on it in the form of coloured strips.

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