Electricity Class 10 Notes Science Chapter 11

Introduction to Electricity - Electricity, Class 10, Science

Electricity

The source of all electricity is charge. As charge is the basis of all electrical phenomena, we need to know the amount of charge on a body. It is measured in coulombs. The coulomb is the SI unit of charge and its symbol is C.

Matter is generally made of protons, electrons and neutrons. Each proton carries a charge of
1.6 × 10^-19 coulomb, and each electron carries an equal negative charge. Neutrons do not carry any net charge. Normally, a body has equal number of protons and electrons, and is therefore, electrically neutral. In certain situations, the balance of charges in a body is disturbed. For example, when a glass rod is rubbed with a silk cloth, some electrons get transferred from the glass rod to the silk. The silk cloth, which gains electrons, becomes negatively charged. And the glass rod, which is left with more protons than electrons, becomes positively charged.

Charged particles or objects can exert forces on each other. While like (similar) charges repel each other, unlike charges attract. Another important thing about charged particles is that they can flow, i.e., they can move in a particular direction. This flow of charged particles is called an electric current. Charged particles such as electrons are present in all substances. But they do not flow on their own. For flow of charges, there has to be a potential difference.

POTENTIAL DIFFERENCE AND THE FLOW OF CHARGE 

The potential difference between two points A and B is the work done per unit charge in taking a charge from B to A. We express this mathematically as

Here, V is the potential difference between the points A and B, and V_A and V_B are the potentials at these points. The potential at infinity is chosen as zero. 

If B be the reference point, the potential at B is V_B = O. From Equation, the potential at A is
V_A = W/q. So, the potential at a point is the work done per unit charge in taking a charge to that point from a chosen reference point. Equation may also be written as

W= qV.

The work done on the charge q is stored as the electric potential energy (U) of the group of charges. So,

U = qV

Unit of potential difference 

The unit of potential difference (and potential) is the volt, whose symbol is 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 between two points is sometimes also called the voltage.

Flow of Charge

Consider two identical metallic spheres P and N, carrying equal amounts of positive and negative charges respectively. A positive charge is to be taken from B to A. It is attracted by the negatively charged sphere N and repelled by the positively charged sphere P. So, to move the charge towards A, one has to apply a force on it towards the left. Thus, the work done is positive. Hence, the potential difference V_A - V_B  is positive. This means V_A > V_B'

As one moves towards P, the work done increases; so, the potential increases. And on moving towards N, the potential decreases. So, the potential of P is higher than that of N. In general, the potential of a positively charged body is taken as higher than that of a negatively charged body

What happens when a free-to-move charge is placed between the spheres? A positive charge will move towards the negatively charged sphere. And a negative charge will move towards the positively charged sphere. That is, a free positive charge moves towards lower potential. And a free negative charge moves towards higher potential.

If the two spheres are connected by a metal wire, electrons from the negatively charged sphere (at a lower potential) will flow to the positively charged sphere (at a higher potential). Eventually, the flow of electrons causes the charges on the spheres to become balanced. When that happens, the spheres no longer carry a net charge, and therefore, have equal potential. So, the flow of electrons stops. So we can say that a potential difference causes charges to flow.

A Cell Provides a Constant Potential Difference

The potential difference provided by things like charged spheres reduces to zero quickly once charges start to flow. So, we have to use cells to provide constant potential difference for a long time. Cells have chemicals inside. Reactions in the cell cause positive and negative charges to gather separately. This creates a potential difference between the terminals of the cell. The terminal at a higher potential is called the positive terminal and the one at a lower potential is called the negative terminal.

The cells that we commonly use are called dry cells (Figure). In a common dry cell, the small metallic cap at one end is the positive terminal, while the flat metallic plate at the other end is the negative terminal. It provides a potential difference of 1.5 V. A cell is represented by the symbol shown in fig (b). The larger line represents the positive terminal, while the shorter line represents the negative terminal.

A combination of cells is called a battery 

Quite often, multiple cells are combined to get a potential difference that is higher than that of a single cell. For example, we connect two 1.5V cells to get a potential difference of 3V (Figure (c)) This is shown using symbols in Figure (d).

ELECTRIC CURRENT

Consider a metallic wire ACB connected across a cell of potential difference V. Since the end A is connected to the positive terminal, it is at a higher potential than the end B. In metals, some electrons are loosely bound to the atoms, and can move within it. These are called free electrons. In the metallic wire, these electrons (negative charges) move from the low-potential side B to the high-potential side A. After reaching A, they enter the cell. The chemical reactions in the cell drive these electrons to the negative terminal. From there, they re-enter the wire at the end B. Thus, there is a continuous flow of electrons in the wire from B to C to A. We say that there is an electric current in the wire. In a metal, the flow of negative charges constitutes the current.

An electric current can also be a flow of positive charges. So, a flow of charge is called an electric current.By convention, the direction of current is taken as the direction of flow of positive charges. Thus, the direction of current is opposite to the direction of flow of negative charges. So, when a wire is connected to a cell, the current in the wire is from the positive-terminal end to the negative-terminal end. 

Measurement of Current

The charge passing per unit time through a given place(area) is the magnitude of the electric current at that place. Thus,

Here Q is the charge that passes through a place in time t.

Unit of current From Equation, we find that current is charge divided by time. The SI unit of charge is the coulomb and that of time is the second. The SI unit of current, therefore, is coulomb / second. This unit is called the ampere, whose symbol is A. Thus, if one coulomb of charge passes through a place in one second, the current there is 1 ampere.

Conductors and Insulators

Materials that conduct electricity easily are called good conductors or simply, conductors. And, materials that do not conduct electricity easily are called insulators.

All metals conduct electricity because they have some loosely bound free electrons, which flow when a potential difference is applied. However, some metals conduct electricity better than others. Silver is the best conductor. But because of the high cost of silver, electric wires are made of copper, or in some cases aluminium.

Most nonmetallic solids do not conduct electricity. Although diamond and graphite are both forms of carbon
(a nonmetal), graphite is a conductor while diamond is an insulator. Insulators do not conduct electricity because their electrons are tightly bound to the atoms. Rubber, plastics, wood, glass and porcelain are some examples of insulators. Insulators have many uses. For example, they are used as protective covers on electric wires and electrician's tools.

Certain liquids also conduct electricity. While distilled water is an insulator, addition of certain salts, acids or bases allows it to conduct electricity. Under normal circumstances, gases do not conduct electricity.

ELECTRIC CIRCUITS AND MEASURING INSTRUMENTS 

A closed path in which a current can flow is called an electric circuit. An electric circuit may have one or more electric elements such as bulbs (or lamps), cells, switches (or plug keys), metal wires, etc. Each element of a circuit has a specific function to play. For example, wires can be used to connect one element to the next. And a plug key or a switch can be used to either complete or break the closed path, thereby starting or stopping the current in the circuit.

Some common circuit elements and their symbols are shown in Figure. 

Fig. Some symbols used in circuit diagrams 

Common Measuring Instruments 

The electric current in a circuit is measured by an instrument called the ammeter, and the potential difference between two points in it is measured by a voltmeter (in voltage stabilizers). In these meters, a needle moving over a graduated scale gives the value of the measured quantity. Each meter has two terminals. The terminal marked '+' is connected by a wire to the higher-potential side of a circuit, while the terminal marked '- ' is connected to the lower-potential side.

Using an ammeter to measure current 

To measure the current through an element of a circuit, an ammeter is connected in such a way that the current flowing through it also flows through the element. Such a connection is called a series connection. In Figure, the current i flowing through the lamp also flows through the ammeter. The reading of the ammeter gives the current through the lamp. Note that if the ammeter is removed, there will be a gap, and the current through the circuit will stop. 

Two or more electric elements are said to be connected in series if the current flowing through one also flows through the rest. 

An ammeter is always connected in series in a circuit. 

Using a voltmeter to measure potential difference 

Figure shows a circuit that has two lamps connected to a cell. We want to measure the potential difference across the lamp L₂, i.e., between the points A and B. As A is on the side of the positive terminal of the cell, its potential is higher than that of B. So, the '+' terminal of the voltmeter is connected to A, and the '- ' terminal, to B. The reading of the voltmeter gives the potential difference across L₂. The current flowing through the voltmeter is different from those flowing through the other elements of the circuit. Also, even if the voltmeter is removed, the current continues to flow in the circuit. Note that the potential difference across L₂ and the voltmeter is the same. Such a connection is called a parallel connection.

Two or more electric elements are said to be connected in parallel if the same potential difference exists across them. 

OHM'S LAW

The electric current through a metallic element or wire is directly proportional to the potential difference applied between its ends, provided the temperature remains constant. 

If a potential difference V is applied to an element and a current i passes through it,

i  ∝  V

or

Thus Ohm's Law V = iR 

Here R is a constant for the given element (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.

Resistance

From equation,

So, for a given potential difference,

Thus, for a given potential difference, the current is inversely proportional to the resistance. The higher is the resistance, the lower is the current. If the resistance is doubled, the current is halved. Good conductors have low resistance, while insulators have very high resistance.

Unit of resistance

Potential difference is measured in volts, and current is measured in amperes. From Equation, R = V/i. So, the unit of resistance is volt/ampere. This unit is called the ohm, and its symbol is W. We can define one ohm as follows.

If a potential difference of 1 volt is applied across an element, and a current of 1 ampere passes through it, the resistance of the element is called 1 ohm.

On What Does Resistance Depend ? 

The resistance of the conductor depends (i) on its length, (ii) on its area of cross-section, and (iii) on the nature of its 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 ∝ ℓ  and R ∝  

Combining eqs. we get

or

Where ρ(rho) is a constant of proportionality and is called electrical resistivity of the material of the conductor. The SI unit of resistivity is Ωm.

SERIES AND PARALLEL CONNECTIONS OF RESISTORS 

A conducting material (e.g., a wire) of a particular resistance meant for use in a circuit is called a resistor. A resistor is sometimes simply referred to as a resistance. It is represented by the symbol . Two or more resistors can be connected in series, in parallel or in a manner that is a combination of these two.

Series Connection of Resistors 

Two or more resistors are said to be connected in series if the current flowing through one also flows through the rest.

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

V=V₁+V₂+V₃

Equivalent resistance in series connection

Figure (a) shows three resistors of resistances R₁, R₂ and R₃ connected in series. The cell connected across the combination maintains a potential difference V across the combination. The current through the cell is i. The same current i flows through each resistor.

Let us replace the combination of resistors by a single resistor R_eq such that the current does not change, i.e., it remains i. This resistance is called the equivalent resistance of the combination, and its value is given by Ohm's law as R_eq = V/i

Thus V = iR_eq. 

The potential differences V₁ , V₂ and V₃ across the resistors R₁ , R₂ and R₃ respectively are given by

Ohm's law as : V₁ = iR₁ , V₂ = iR₂ , V₃ = iR₃

Since the resistors are in series, V = V₁ + V₂ + V₃

Substituting the values of the potential differences in the above equation,

iR_eq = iR₁ + iR₂ + iR₃

or iR_eq =i(R₁ +R₂ +R₃)

or

Similarly, for n resistors connected in series,

Equivalent resistance of resistors in series :

Parallel Connection of Resistors

The total current flowing into the combination is equal to the sum of the currents passing through the individual resistors.

If resistors are connected in such a way that the same potential difference gets applied to each of them, they are said to be connected in parallel.

Equivalent resistance in parallel connection 

Figure (a) shows three resistors of resistances R₁,  R₂ and R₃ connected in parallel across the points A and B. The cell connected across these two points maintains a potential difference V across each resistor. The current through the cell is i. It gets divided at A into three parts i₁, i₂ and i₃, which flow through R₁, R₂ and R₃ respectively.

Let us replace the combination of resistors by an equivalent resistor R_eq such that the current i in the circuit does not change (Fig). The equivalent resistance is given by Ohm's law as R_eq = V/i.

Thus,

The currents i₁ , i₂ and i₃ through the resistors R₁, R₂ and R₃ respectively are given by Ohm's law as

Since the resistors are in parallel,

i = i₁ + i₂ + i₃

Substituting the values of the currents in the above equation,

or

Similarly, if there are n resistors connected in parallel, their equivalent resistance R_eq is given by

 Equivalent Resistance of resistors in parallel :

 For two resistances R₁ and R₂ connected in parallel,

 or R =

The equivalent resistance in a parallel connection is less than each of the resistances.

When a resistance is joined parallel to a comparatively smaller resistance, the equivalent resistance is very close to the value of the smaller resistance.

Note : If a resistor connected in series with others is removed or fails, the current through each resistor becomes zero. On the other hand, if a resistor connected in parallel with others fails or is removed, the current continues to flow through the other resistors.

Distribution of Current in Two Resistors in Parallel

Consider the circuit in fig. The resistors R₁ and R₂ are connected in parallel. The current i gets distributed in the two resistors.

i = i₁ + i₂ .....(i)

Applying Ohm's law to the resistor R₁           

V_A - V_B =R₁i₁· .....(ii)

And applying Ohm's law to the resistor R₂

V_A - V_B = R₂i₂ .... (iii)

From (ii) and (iii), R₁i₁ = R₂i₂ or

Substituting for i₂ in (i), we have

i = i₁ +

or

Similarly,

Thus,

The current through each branch in a parallel combination of resistors is inversely proportional to its resistance.

Devices in Series and Parallel

You must have seen tiny bulbs strung together for decorating buildings during festivals like Diwali, and occasions like marriages, etc. These bulbs are connected in series, and the mains voltage is applied to the combination. The potential difference (V) of the mains gets divided across the bulbs (V = V₁ + V₂ + V₃ + ... ). So, a small potential difference exists across each bulb, close to that required to make the bulb work. However, the same current flows through all the bulbs. So, if one bulb goes bad, the current through it stops, and this stops the current through the rest of the bulbs as well. To make the chain of lights work, we have to find and replace the defective bulb. This problem does not occur with the lights in our house. That is because in houses, lights, fans, etc., are connected in parallel. In parallel connection, the same mains voltage gets applied to each device, but the current through each is different. If one of them goes bad, the current in the other branches of the parallel connection does not stop. Another advantage of parallel connection is that, unlike series connection, each device can draw a different current, as per its requirement.

HEATING EFFECT OF ELECTRIC CURRENT 

When an electric current passes through a bulb, the filament gets so hot that it glows and emits light. When a current passes through the filament of an electric iron, the iron becomes very hot. This increase in temperature is due to what is called 'the heat produced due to current'.Suppose a resistor R is connected to a cell. The cell maintains a potential difference V across the resistor, driving a current i through it.

So, V = iR  ......(i)  

The current through the resistor is actually a flow of negative charges (electrons). Inside the cell, the negative charges flow from the positive to the negative terminal. The cell does work = QV to take a charge through the potential difference V between its terminals. This increases the energy of the charge by QV. This increased energy gets converted to heat in the resistor. So, the energy appearing as heat is given by

U = QV ......(ii)

The charge that passes through the wire in time t is

Q =it.  ......(iii)

Using (i), (ii) and (iii), we find that the heat produced in the wire in time t is

U =QV = (it) (iR) =i² Rt.

From Equation the heat produced is proportional to the square of the current, if R and t remain constant. So, if the current passing for a given time through a given resistance is doubled, the heat produced becomes four times. Similarly, for a given i and t, the heat produced is proportional to R. If the same current i passes through two resistances in a given time, more heat will be produced in the larger resistance. The heat produced can also be written as.

U = i²Rt =

or U =

For a given V and t, the heat produced is inversely proportional to R. So, if the same potential difference is applied across two resistances, more heat will be produced in the smaller resistance.

We have seen above that the increased energy of a charge gets converted to heat in the resistor. The increase in energy comes from the work done by the cell. This uses up the chemical energy of the cell. So, the energy appearing as heat in the resistor ultimately comes at the expense of the chemical energy of the cell.

Not always is the work done by a cell converted to heat. Immediately after a motor is connected to a cell, the speed of the shaft of the motor increases. A part of the work done by the cell goes into producing the increase in kinetic energy. And a part is used to overcome friction, etc. When the motor achieves a constant speed, its kinetic energy does not change. So the work done by the cell is only used to overcome friction, etc. This appears as heat. That is why the cover over a motor becomes warm on use.

Electric Power 

Power is the rate of doing work, or the rate at which energy is produced or consumed. The electrical energy produced or consumed per unit time is called electric power. In an electric circuit, the power is

P =

Using iR = V

P = Vi

P =

The energy consudmed and power are realted as

U = Pt.

Unit of Power

The SI unit of energy is the joule, and that of time is the second. The SI unit of power is therefore joule/second. This unit is called the watt, whose symbol is W.

Applications of the Heating Effect of Current

The heating effect of electric current has many uses. Electric bulbs, room heaters, electric irons, immersion heaters, toasters, electric fuses and a number of other appliances work on this principle. In all of these, a wire of suitable resistance, commonly called the heating element, is connected to the power supply. The current passing through the element produces heat in it, which is used for some specific purpose.

Electric bulb

An electric bulb has a simple structure. It consists of a sealed glass bulb that has a tungsten filament connected to two electrical contacts. The bulb is filled with an unreactive gas like argon or nitrogen. To produce white light, the filament has to be heated to about 3000°C by passing a current through it. Obviously, the material of the filament should such that it does not melt at this temperature. Tungsten is used for the filament because its melting point is about 3400°C. The sealed glass bulb serves two purposes. First, it protects the filament from oxidation and the effects of humidity. Secondly, the small enclosed volume makes it easier to maintain the required temperature, as without it the loss of heat would be more.

Fuse 

A fuse is a safety device that does not allow excessive current to flow through an electric circuit. It consists of a metallic wire of low melting point, fixed between the two terminals of a fuse plug. The fuse plug fits into a fuse socket connected in the circuit. Fuses are available in various shapes. The fuse plug is used in household wiring. It is made of porcelain.

A fuse is connected in series with an appliance (such as a TV) or a group of appliances (such as the lights and fans in a room). So, the current through the fuse is the same as the current through the appliance or the group of appliances. If this current exceeds a safe value, the heat produced in the fuse wire causes it to melt immediately. This breaks the circuit, preventing any damage. Figure shows examples of how a fuse is connected in circuits.

Good-quality fuse wires are made of tin, as it has a low melting point. Some fuse wires are made of an alloy of tin and copper. The thickness of the fuse wire depends on the circuit in which it is to be used. If a section of the circuit is meant to carry a maximum of 5A current, the fuse wire should also be able to carry currents up to
5A. Similarly, for wiring meant for 15A, the fuse wire should be thicker, and should be able to carry currents up to 15A.

Disadvantages of the Heating Effect of Current

A current always produces some heat, whether we use the heat or not. If the heat produced cannot be utilized, it represents a wastage of energy. A considerable amount of energy is thus wasted in the transmission of electricity from the generating station to our homes. Sometimes, the heat produced in a device is so much that it can damage the device, unless proper cooling arrangements are made. To dissipate the heat produced in TV sets, monitors, etc., their cabinets have grills for air to pass. Certain components of a computer get so hot that they have fans to cool them.

Rating of Electric Appliances

Take an electric bulb and see what is written on it. Apart from the name and the symbol of the company, we will find values of power and potential difference. For example, it could be 60W, 220V. It means that 220V should be applied across this bulb, and when 220V is applied, the power consumed will be 60W. We will find similar markings on all electric· appliances. For an electric appliance, the values of power and voltage taken together form what is called the rating of the appliance. From the rating of an appliance, you can easily calculate its resistance by using the equation P = . Note that higher the power rating, smaller the resistance. So, a 1000W heater has less resistance than a 100W bulb. We can also calculate the current drawn by an appliance by using the relation i = .

Kilowatt hour

Power is the rate of energy consumed or produced. If 1 joule of energy is used per second, the energy is used at the rate of 1 watt. In other words, if energy is used at the rate of 1 watt, the total energy used in 1 second is 1 joule. How much energy is used in 1 hour if it is used at the rate of 1000 watt?

It is (1000 watt) × (3600 second) = 3,600,000 joule.

This amount of energy is called 1 kilowatt hour, written in short as kWh. Thus, 1 kWh =3,600,000 J = 3.6 × 10⁶J. The electrical energy used in houses, factories, etc., is measured in kilowatt hours. The cost of electricity is fixed per kilowatt hour. One kilowatt hour of electrical energy is called one unit.