Electricity

Class 10 Science

Electricity has an important place in modern society. It is a controllable and convenient form of energy for a variety of uses in homes, schools, hospitals, industries and so on.

Electric Current

If the electric charge flows through a conductor (for example, through a metallic wire), we say that there is an electric current in the conductor.

Electric current is expressed by the amount of charge flowing through a particular area in unit time. It is the rate of flow of electric charges. In circuits using metallic wires, electrons constitute the flow of charges.

In an electric circuit the direction of electric current is taken as opposite to the direction of the flow of electrons, which are negative charges.

If a net charge Q, flows across any cross-section of a conductor in time t, then the current I, through the cross-section is

$$ I = \frac{Q}{t} $$

The SI unit of electric charge is coulomb (C), which is equivalent to the charge contained in nearly 6 × 10¹⁸ electrons. The electric current is expressed by a unit called ampere (A). One ampere is constituted by the flow of one coulomb of charge per second.

Electric Potential and Potential Difference

For flow of charges in a conducting metallic wire, the electrons move only if there is a difference of electric pressure, called the potential difference, along the conductor. This difference of potential may be produced by a battery, consisting of one or more electric cells. The chemical action within a cell generates the potential difference across the terminals of the cell, even when no current is drawn from it. When the cell is connected to a conducting circuit element, the potential difference sets the charges in motion in the conductor and produces an electric current. In order to maintain the current in a given electric circuit, the cell has to expend its chemical energy stored in it.

Electric potential difference between two points in an electric circuit carrying some current is defined as the work done to move a unit charge from one point to the other.

Potential difference (V) between two points = Work done (W)/Charge (Q)

$$ V = \frac{W}{Q} $$

The SI unit of electric potential difference is volt (V). One volt is the potential difference between two points in a current carrying conductor when 1 joule of work is done to move a charge of 1 coulomb from one point to the other.

The potential difference is measured by means of an instrument called the voltmeter. The voltmeter is always connected in parallel across the points between which the potential difference is to be measured.

Ohm's Law

The potential difference, V, across the ends of a given metallic wire in an electric circuit is directly proportional to the current flowing through it, provided its temperature remains the same. This is called Ohm’s law.

$$ V \propto I $$

$$ V = IR $$

R is a constant for the given metallic wire at a given temperature and is called its resistance. It is the property of a conductor to resist the flow of charges through it. Its SI unit is ohm, represented by the Greek letter Ω.

$$ R = \frac{V}{I} $$

$$ I = \frac{V}{R} $$

The current through a resistor is inversely proportional to its resistance. If the resistance is doubled the current gets halved. In many practical cases it is necessary to increase or decrease the current in an electric circuit. A component used to regulate current without changing the voltage source is called variable resistance. In an electric circuit, a device called rheostat is often used to change the resistance in the circuit.

Factors on which Resistance of a Substance Depends

The resistance of the conductor depends on

Length
Area of cross-section
Nature of material

Resistance of a uniform metallic conductor is directly proportional to its length (l) and inversely proportional to the area of cross-section (A).

$$ R \propto \frac{l}{A} $$

$$ R = \rho \frac{l}{A} $$

where ρ (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor. The SI unit of resistivity is Ω m. It is a characteristic property of the material. The metals and alloys have very low resistivity. They are good conductors of electricity. Insulators like rubber and glass have high resistivity. Both the resistance and resistivity of a material vary with temperature.

System of Resistors

There are two methods of joining the resistors together - series and parallel.

Resistors in Series

In a series combination of resistors the current is the same in every part of the circuit or the same current through each resistor.

The total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors.

$$ V = V_1 + V_2 + V_3 $$

$$ IR = IR_1 + IR_2 + IR_3 $$

$$ R_{\text{s}} = R_1 + R_2 + R_3 $$

When several resistors are joined in series, the resistance of the combination R_s equals the sum of their individual resistances, R₁, R₂, R₃, and is thus greater than any individual resistance.

Resistors in Parallel

The total current I, is equal to the sum of the separate currents through each branch of the combination.

$$ I = I_1 + I_2 + I_3 $$

$$ \frac{V}{R} = \frac{V}{R_1} + \frac{V}{R_2} + \frac{V}{R_3} $$

$$ \frac{1}{R_{\text{p}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} $$

The reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.

Heating Effect of Electric Current

If the electric circuit is purely resistive, that is, a configuration of resistors only connected to a battery; the source energy continually gets dissipated entirely in the form of heat. This is known as the heating effect of electric current. This effect is utilised in devices such as electric heater, electric iron, etc.

Consider a current I flowing through a resistor of resistance R. Let the potential difference across it be V. Let t be the time during which a charge Q flows across. The work done in moving the charge Q through a potential difference V is VQ. Therefore, the source must supply energy equal to VQ in time t. Hence the power input to the circuit by the source is

$$ P = \frac{VQ}{t} = VI $$

The amount of heat H produced in time t is

$$ H = VI t $$

Applying Ohm’s law, we get

$$ H = I^2 R t $$

This is known as Joule’s law of heating. The law implies that heat produced in a resistor is (i) directly proportional to the square of current for a given resistance, (ii) directly proportional to resistance for a given current, and (iii) directly proportional to the time for which the current flows through the resistor.

Practical Applications of Heating Effect of Electric Current

Heating effect of electric current has many useful applications. The electric laundry iron, electric toaster, electric oven, electric kettle and electric heater are some of the devices based on Joule’s heating.

The electric heating is also used to produce light, as in an electric bulb. Here, the filament must retain as much of the heat generated as is possible, so that it gets very hot and emits light. It must not melt at such high temperature. A strong metal with high melting point such as tungsten (melting point 3380°C) is used for making bulb filaments. The filament should be thermally isolated as much as possible, using insulating support, etc. The bulbs are usually filled with chemically inactive nitrogen and argon gases to prolong the life of filament. Most of the power consumed by the filament appears as heat, but a small part of it is in the form of light radiated.

Another common application of Joule’s heating is the fuse used in electric circuits. It protects circuits and appliances by stopping the flow of any unduly high electric current. The fuse is placed in series with the device. It consists of a piece of wire made of a metal or an alloy of appropriate melting point, for example aluminium, copper, iron, lead etc. If a current larger than the specified value flows through the circuit, the temperature of the fuse wire increases. This melts the fuse wire and breaks the circuit.

Electric Power

Electric power is the rate at which electric energy is dissipated or consumed in an electric circuit.

$$ P = VI $$

$$ P = I^2 R $$

$$ P = \frac{V^2}{R} $$

The SI unit of electric power is watt (W). It is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V.

The commercial unit of electric energy is kilowatt hour (kW h), commonly known as ‘unit’.

1 kW h = 1000 watt × 3600 second

= 3.6 × 10⁶ watt second

= 3.6 × 10⁶ joule (J)