1 ELECTRICITY 1.1 INTRODUCTION Electricity is one of the most important sources of energy in the modern world. All appliances such as lights, fans, torch, geysers, air-conditioners, televisions, computers, mobile phones, etc. reuire electricity to work. It finds immense use in homes, industries, schools, hospitals, etc. For a source of energy that is indispensable to us, it becomes almost mandatory to learn about it. This is what we are going to do in this chapter. 1.2 ELECTRIC CHARGE The source of all electricity is electric charge. It is defined as the fundamental property of matter that causes it to experience a force (attraction or repulsion) in the presence of other matter. Unit : The SI unit of charge is coulomb and is denoted by C. Examples : If we scatter very tiny bits of paper on a table and bring a plastic comb near them, nothing happens. But when we run the comb through dry hair several times and then bring the comb near the paper bits, they start getting attracted to it. The comb is said to have got electrically charged (when we ran it through dry hair) due to which it exerts a force (of attraction) on the tiny bits of paper. Similarly, a glass rod rubbed with a silk cloth or an ebonite rod rubbed with a woolen cloth attracts tiny bits of paper. There are two types of electric charges positive and negative. By convention, the glass rod in the above example is said to be positively charged while the ebonite rod is said to be negatively charged. An important property of charges is that like charges (positive positive or negative negative) repel each other and unlike (positive negative) charges attract. Explanation : As you know, matter is made up of atoms that in turn are made up of electrons, protons and neutrons. An electron carries a negative charge of 1.6 10-19 C, a proton carries an eual positive charge and a neutron carries no net charge. Since a substance usually has eual number of electrons and protons, it is electrically neutral. hen the balance of the number of electrons and protons in a body gets disturbed due to some factor (like rubbing of one substance with another in our examples), it gets charged. hen a glass rod is rubbed with a silk cloth, the loosely bound electrons in the rod get transferred to the silk cloth. The glass rod, therefore, has more protons than electrons, making the rod positively charged. On the other hand, the silk cloth gains electrons from the rod and becomes negatively charged. In the case of plastic comb/ebonite rod, the comb/rod gains electrons from the hair/woolen cloth making the comb/rod negatively charged and the hair/woolen cloth positively charged. [hich body loses electrons and which one gains electrons depends on the atomic properties of that body.] Now consider any single tiny bit of paper we used in our example. It is neutral because it has eual number of electrons and protons. hen the glass rod is brought close to it, the rod starts attracting electrons in the bit of paper to that portion which is nearer to the rod. This happens because unlike charges (rod is positively charged and electrons are negatively charged) attract. This eventually causes the bit of paper to become negatively charged on the end nearer to the rod due to excess of electrons on that end. Again as we know, unlike charges attract, Therefore the bit of paper gets attracted to the rod. One thing to note here is that the bit of paper always remains neutral overall. It is just that one portion becomes negatively charged while the other portion becomes eually positively charged.
1.2 CBSE PHYSICS FOR CLASS X hen the plastic comb or ebonite rod is brought close to an independent bit of paper, the comb/rod repels the electrons in the paper away from the portion closer to the comb/rod. This is because like charges (the comb/ rod and electrons are both negatively charged) repel. This eventually causes the bit of paper to become positively charged on the end nearer to the comb/rod due to deficit of electrons on that end. Since unlike charges attract, the bit of paper again gets attracted to the comb/rod. Example 1. Calculate the number of electrons constituting one coulomb of charge. Solution : e know that the charge on one electron is 1.6 10 19 C In other words, number of electrons constituting a charge of 1.6 10 19 C = 1 1 10 Number of electrons constituting a charge of 1 C 6.25 10 19 1.6 10 1.6 1.2.1 PROPERTIES OF ELECTRIC CHARGES Following are the properties of electric charges : (i) (iii) Like charges repel each other while unlike charges attract. 19 18 [NCERT] Electric charge is conserved. It can neither be created nor destroyed. The net charge (algebraic sum of positive and negative charges) in an isolated system is constant. Total charge on any body is an integral multiple of the charge on an electron or proton (i.e. 1.6 10-19 C). In other words, electric charge is uantized. [Elementary particles called uarks are exception to this property. They carry charges that are integral multiples of one-third the charge on an electron or a proton. e will not discuss uarks here because it is beyond the scope of this book.] 1.3 ELECTRIC POTENTIAL AND POTENTIAL DIFFERENCE 1.3.1 ELECTRIC POTENTIAL Consider a situation in which there is a group of stationary charges as shown in Figure 1.2. hen a charge is placed at some point 2, the group of charges will exert a force on it. Therefore work needs to be done if this charge has to be moved from point 2 to point 1. If point 2 is at infinity and is a unit positive charge, then the work done in moving the charge from point 2 to point 1 is the electric potential at point 1. Electric potential at a point is thus defined as the work done in moving a unit positive charge from infinity to that point. Infinity is the reference point here (just like we have the Origin (0, 0) as the reference point in Coordinate Geometry). The potential at infinity is assumed to be zero and the potentials at all other points are calculated with respect to it. 1.3.2 POTENTIAL DIFFERENCE For all practical purposes however, potential difference between two points is more commonly used than potential at a point. Potential difference between two points 1 and 2 is the work done in moving a unit positive charge from point 2 to point 1. If be the work done in moving charge from point 2 to point 1, the potential difference, V between points 1 and 2 will be given by, V1 V2 V where V 1 and V 2 are the potentials at points 1 and 2 respectively. Note : hen point 2 is at infinity, V 2 = 0 V1 V2 V1 [From euation (1)] (1)
ELECTRICITY 1.3 Unit : The SI unit of potential and potential difference is volt (named after an Italian physicist Alessandro Volta) and is denoted by the symbol V. From euation (1), 1 joule 1Volt or 1V 1JC 1coulomb 1 Thus, the potential difference between two points is one volt if one joule of work is done in moving one coulomb charge from one point to the other. The potential difference is measured by an instrument called voltmeter. It is always connected in parallel to the electric element or the two points across which potential difference is to be measured. Voltmeters are discussed in Section 1.7 of this chapter. Potential difference (or voltage as it is sometimes called) is important in the field of electricity because it causes the flow of charges. Example 2. How much is the work done in moving a charge of 4 C across two points having a potential difference of 24 V? Solution : e know that, potential difference, V V1 V2 or V Here, potential difference, V = 24 V, charge moved, = 4 C. e have to calculate the work done, From the formula, reuired work done, = V = 4 C 24 V = 96 joules or 96 J Example 3. hat is the work done in moving a charge of 2 C from a point at 220 V to a point at 120 V? Solution : e know that, potential difference, V V1 V2 or V Here, = 2 C. Assuming V 1 = 220 V and V 2 = 120 V, we have Potential difference, V = V 1 V 2 = 220V 120 V = 100 V Now, we have to calculate the work done, From the formula, the reuired work done, = V = 2 C 100 V = 200 J Example 4. How much energy is given to each coulomb of charge passing through a 6 V battery? [NCERT] Solution : e know that, potential difference, V or V Here, = 1 C and V = 6 V [since the charge is passed through the battery having potential difference across its terminals eual to 6 V] Now, the work done in moving this charge through the battery, = V or = 1 C 6 V = 6 J This work done on the charge on moving it through the battery will be the amount of energy transferred to the charge. Therefore, the reuired amount of energy given to the charge = 6 J Example 5. 500 joules of work is done in transferring 40 coulombs of charge from one terminal of a battery to the other. hat is the battery voltage? Solution : Battery voltage is another term used for the potential difference across the terminals of a battery. Now, battery voltage = potential difference, Given : = 500 J and = 40 C Reuired battery voltage, 1.3.3 FLO OF CHARGES 500 J V 40 C V 12.5 V Consider a glass vessel with two arms, P and Q separated by a valve and filled with water as shown in Figure 1.3. The water level in arm Q is kept higher than that in arm P with the valve closed. The pressure at point B
1.4 CBSE PHYSICS FOR CLASS X is due to water in arm Q (and the atmospheric pressure) whereas the pressure at point A is due to water in arm P (and the atmospheric pressure). e know that the pressure exerted by a column of liuid is directly proportional to the height of the column. Therefore, pressure at point B is higher than that at point A (the atmospheric pressure is common at both points; so we can cancel it out). So, we can say that there is a pressure difference between points A and B. As soon as the valve is opened, water flows from B to A till the heights in both the arms become eual and there is no pressure difference. So, the water flowed from the point at higher pressure to the point at lower pressure, only until there was a pressure difference between the two points. Similarly, charges flow only when there is an electric pressure difference or potential difference between two points. Also, a free positive charge flows from the point at higher potential to the point at lower potential while a free negative charge flows from the point at lower potential to the point at higher potential. To understand the flow of charges, let us consider two metallic bodies A and B as shown in Figure 1.4. A is positively charged and B is eually negatively charged. hen we move a positive charge from B to A, positive work needs to be done to overcome the attractive force by B and the repulsive force by A on the charge. From euation (1), ve VA VB ve 0 or VA VB 0 ve Hence, V A > V B Therefore, a positively charged body (A) is at a higher potential than a negatively charged body (B) and a potential difference between the two bodies exists. If a positive charge is placed between the two bodies, it will experience a force of attraction from B and a force of repulsion from A. Both these forces will make the charge move from A to B thus proving our point that a free positive charge flows from a higher potential to a lower potential. If a negative charge is placed between the two bodies, it will flow from B (lower potential) to A (higher potential) because of similar reasons. hen A and B are now connected by a metal wire, electrons flow through the wire from the negatively charged body B to the positively charged body A, (i. e. from the body at lower potential to the body at higher potential) till A and B are neutral and there is no potential difference between the two. So we can say that electrons flow only until there is a potential difference between the two ends of the wire (similar to water flowing only until there was a pressure difference between two points). One thing to note here is that only electrons (negative charges) flow and not protons (positive charges). This is because electrons are loosely bound to the atoms in many substances (called conductors which we will discuss later in the chapter) and are free to flow. On the other hand, protons are tightly bound to the nuclei of atoms and cannot flow freely. If they could, protons would have flowed from A to B (i. e. from the body at higher potential to the body at lower potential). In the above example, the flow of charges stopped because the potential difference between A and B became zero after some time. If we could maintain a constant potential difference between the two ends of the metal wire, charges would have continued to flow for a long time. A constant potential difference across the ends of a wire (or any other conductor) is maintained by a cell. The chemical reactions inside a cell make positive charges collect on one terminal and negative charges collect on the other. As discussed before, the positive terminal is at higher potential while the negative terminal is at lower potential. hen a metal wire is now connected across these terminals, a potential difference is created between the two ends of the wire (just like in our example discussed before). Electrons therefore, flow from the negative to the positive terminal through the wire. In our day-to-day lives, dry cells are commonly used to maintain a constant potential difference. An example of a dry cell shown in Figure 1.5 provides a potential difference of 1.5 V.
The figure also shows how a cell is represented in diagrams. The longer line denotes the positive terminal and the shorter one denotes the negative terminal of the cell. A combination of cells, called battery, is often used to get a higher potential difference than we would get from a single cell. In a battery, multiple cells are connected one after the other (in series) and the total potential difference across the terminals of the battery or the combination is the sum of individual voltages (potential differences) of the cells. For example, two 1.5 V dry cells are often used in combination as a battery in a torch to give a total potential difference of 3 V. ELECTRICITY 1.5 Example 6. Four 1.5 V cells are connected in series and used as a battery in a circuit as shown in the figure. hat is the potential difference across the terminals of the battery? Also calculate the energy gained by a 2 C charge in passing through (i) (iii) one cell two consecutive cells the battery Solution : e know that when multiple cells are connected in series as shown in the figure, the total potential difference across the terminals of the combination will be eual to the sum of individual voltages of the cells. Therefore, the potential difference across two cells will be eual to 1.5 V + 1.5 V = 3 V And, the potential difference across the battery terminals (i.e. the potential difference across the combination of four cells) will be eual to 1.5 V + 1.5 V + 1.5 V + 1.5 V = 6 V (i) Note : Now, the energy gained by a 2 C charge in passing through one cell, i.e. through a potential difference of 1.5 V will be given by, = V = 2 C 1.5 V = 3 J Similarly, the energy gained by the given charge in passing through two consecutive cells, i.e. through a potential difference of 3 V will be given by, = V = 2 C 3 V = 6 J And the energy gained by the given charge in passing through the terminals of the battery, i.e. through a potential difference of 6 V will be given by, = V = 2 C 6 V = 12 J e have said that the potential difference across the combination of cells connected in series is eual to the sum of individual potential differences of the cell. This is true only when the cells are connected in such a way that the negative terminal of each cell is connected with the positive terminal of the next cell. In fact, the potential difference across the combination of cells is the algebraic sum of the individual voltages of the cells. So, if we take two (say) cells and connect the negative terminal of one cell to the negative terminal of the other cell, the potential difference across the combination of these two cells will be the algebraic sum of the individual potential differences. If the two cells have eual voltages, they will cancel each other and the net potential difference across the combination will be zero. This is the reason why the bulb of a torch using two cells in series does not glow if the cells are inserted in such a way that negative terminals of the individual cells are connected to each other. The next example makes the situation clearer. Example 7. Two 1.5 V cells, A and B are connected in a circuit across two points X and Y as shown in the figure. hat is the potential difference across the terminals of the given combination of cells? Calculate the energy gained by a charge of 4 C in moving through the combination. Solution : e need to calculate the potential difference across the combination of two cells, i.e V X Take a point P between the two cells as shown in the figure. Now, V X = V X + V P [adding and subtracting V P ] = (V X ) + (V P ) [rearranging the terms] (A)
1.6 CBSE PHYSICS FOR CLASS X e know that the potential difference or voltage of the cell is the potential difference between its positive and negative terminals. and V X = 1.5 V [for the first cell] V Y = 1.5 V [for the second cell] or V P = 1.5 V From euation (A), V X = (V X ) + (V P ) = 1.5 V + ( 1.5 V) = 0 Thus, the reuired potential difference across the terminals of the combination of cells = 0 V e know that the energy gained, by any charge, in moving through a potential difference, V is given by, = V In this case, = 4 C, V = 0 V. From the formula, the energy gained, = 4 C 0 V = 0 Second method : The fact that the energy gained by the charge will be zero can be understood using another logic. hen the charge of 4 C moves from the positive terminal of first cell to its negative terminal, the positive terminal repels while the negative terminal attracts the charge. So, it gains some energy, 1 given by 1 = V = 4 C 1.5 V = 6 J. Now, when the same charge moves from the negative terminal of the second cell to its positive terminal, it moves through a potential difference of 1.5 V. So, it gains energy, 2 given by 2 = 4 C ( 1.5 V) = 6 J The negative energy gained can be explained by the fact that the negative terminal attracts while the positive terminal repels the charge, and hence resists the charge from reaching the positive terminal of the second cell. Thus, the charge loses energy in overcoming the forces against its movement. Therefore, the total energy gained by the charge will be 1 + 2 = 6 J + ( 6 J) = 0 1.4 ELECTRIC CURRENT AND CIRCUIT 1.4.1 ELECTRIC CURRENT hen water flows in a river, we say that there is water current. Similarly, when charges flow in a conductor, we say that there is an electric current in the conductor. So, flow of charge (positive or negative) is called an electric current. Direction of current : Let us connect a metal wire across the terminals of a dry cell as shown in Figure 1.6. The positive terminal of the cell is at a higher potential than its negative terminal (refer Section 1.3.3). Therefore, the end of the wire that is connected to the positive terminal of the cell will be at a higher potential than the end connected to the negative terminal. So, there is a potential difference set up across the two ends of the wire. e know that the metal wire has loosely bound electrons called free electrons that are free to move within the wire. Since these electrons are negatively charged, they will flow from the end of the wire at lower potential to the end of the wire at higher potential, i. e. from the negative to the positive terminal of the cell, causing an electric current to flow in the wire. At the positive terminal of the cell, the electrons enter it. The chemical reactions occurring inside the cell forces these electrons towards the negative terminal from where they re-enter the wire and follow the same cycle again. This is how we get a continuous flow of current in the wire. Conventionally, the direction of electric current is taken as the direction of flow of positive charges. This means that the direction of electric current is opposite to that of flow of negative charges (or electrons). So, we can say that the direction of current in the wire when it is connected to a cell, is from the positive-terminal end to the negative-terminal end as shown in the figure. Magnitude of current : Coming to the magnitude of current, the magnitude of current is defined as the charge passing per unit time through a particular area. If a charge of Q coulomb flows through an area in time t seconds, the magnitude of electric current flowing through that area is given by,