Electrical quantities and Components

ELECTRICAL QUANTITIES

As pictured today, the continuous flow of electrons through a medium constitutes an electric current. Some substances such as copper and aluminium act as very good conductors of electricity and offer very little hindrance to the flow of electrons (flow of current).

Some other substances such as rubber and porcelain offer high resistance to the flow of electrons and hence to the flow of current. These are known as insulators. Materials like germanium, silicon-carbide etc., whose resistance at ordinary temperature lies in between conductors and insulators, are called semi-conductors.

Electric Current (I)

The charge of an electron is e = 1.6 × 10^-19 Coulombs and is negative.

Electric current is defined as rate of flow of electric charge.

i = dq/dt ampere     ….. (1)

where q is the charge in Coulombs.

The unit of current is the ampere, which represents one coulomb of charge transferred in one second. The direction of current flow depends on the flow of charge. If 'Q' coulombs of charge are continuously transferred every T seconds, we may write equation (1) as

I = Q/T   …… (2)

Electric Potential (E or V)

This is generally measured between two points and its unit is the volt. If the work done in moving a charge of one coulomb between the two points is one joule, then we say that the potential of one point with reference to the second point is one volt.

Vor E= dW / dQ …… (3)

where W is the work done in joules.

Electrical Resistance (R)

The resistance of a circuit is the property by which it opposes the flow of current. This parameter, measured in Ohms, is responsible for energy dissipation. The Ohm is defined as the resistance (at zero degree centigrade) of a column of mercury of uniform cross-section having a length of 106.3 cm and a mass of 14.4561 grams.

The resistance of a conductor depends on (a) its length, (b) the cross-sectional area, (c) the material of the conductor (d) the temperature. Usually, the resistance is given per unit cross-section and unit length. This is called specific resistance or resistivity of the material represented by the letter, p. The resistivity of aluminium is 0.0283 μ Q-m while that of copper is 0.0173 μ 2-m. The resistance of a material is given by

R =  ρl / ɑ    ………. (4)

where 'l' is the length and 'a' is the area of cross-section.

In SI units, 'ρ ' is in Ohm-m, while 'l' is in m and 'a' is in sq-m

Electrical Conductance (G)

The reciprocal of resistance is called conductance. Its unit is Siemen and its symbol is G.

G = 1/R

Similarly, the reciprocal of resistivity is called conductivity. Its symbol is ɑ.

ɑ = 1/ρ Siemen/metre

EXAMPLE 1: A copper wire is 500 m long and has a diameter of one mm. Find its resistance if the resistivity of copper is 1.73 × 10^-8 Ω-m.

Solution

EXAMPLE 2: A copper wire of given length and diameter has a resistance of R Ohms. It is drawn successfully through dies till its diameter is half the previous value. Assuming that the resistivity remains unchanged, find the new resistance.

Solution

Let the given length be l₁ and diameter d₁. Total volume of copper in the wire

= πd²₁ l₁ / 4

This remains unchanged even after passing through dies.

If the new length is l₂, (the diameter being d₁ / 2 )

EXAMPLE 3: An aluminium wire 400 meters long has a resistance of 0.25 Ohm. Find its area of cross-section. Find the area of cross section required if the wire is of copper (specific resistances of copper and aluminium are 1.73 x 10-8 and 2.83 × 10−8 Ohm-m respectively).

Solution

BASIC CIRCUIT COMPONENTS

The three basic circuit components are

1. Resistor

2. Capacitor and

3. Inductor

Resistor

Resistor is an electrical component made from the material which opposes the flow of current through it. Figure 1.1 shows symbol of resistor. It is denoted as 'R'. The unit of resistance is Ohm (Ω).

The relation between voltage and current is given by Ohm's law.

Energy dissipated in the resistor in the form of heat. It is given by

P = VI = (IR)I = I² R = V² / R watts.

Resistor converts amount of energy into heat during time t and it is given by

= V.I.t joules

Capacitor

Capacitor is a storage element which can store and deliver energy in an electric field. The capacitor is denoted as 'C'. The unit of capacitance is Farad (F). Figure 1.2 shows the symbol of capacitor.

Any two metal plates between which an electric field can be maintained constitute a capacitor.

Inductor

Inductor is an element in which energy can be stored in the form of electromagnetic field. Figure 1.3 shows symbol of inductor. It is denoted as L. It is measured in Henry (H).

It is like a coil wound on a magnetic core or may be air core.