# CHAPTER 1 ELECTRICITY

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1 CHAPTER 1 ELECTRICITY Electric Current: The amount of charge flowing through a particular area in unit time. In other words, it is the rate of flow of electric charges. Electric Circuit: Electric circuit is a continuous and closed path of electric current. Note: Conventionally, 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 Expression of Electric Current Electric current is expressed by the rate of flow of electric charges. Rate of flow means the amount of charge flowing through a particular area in unit time. If a net electric charge (Q) flows through a cross section of conductor in time t, then; Where, I - electric current, Q- net charge and t - time in second. SI unit of the electric charge is coulomb (C), SI unit of time is second (s). SI unit of electric current is ampere (A). Definition of one ampere One ampere is constituted by the flow of one coulomb of charge per second. This means if 1 coulomb of electric charge flows through a cross section for 1 second, it would be equal to 1 ampere. Therefore; 1A = or 1A = 1Cs -1 Note: 1. Smaller unit of electric current 1mA (milliampere) = 10 3 A 1μA(microampere) =10 6 A

2 2. Ammeter: An apparatus to measure electric current in a circuit. It is always connected in series in a circuit. Que: How many electrons make one coulomb of charge? Ans: One coulomb (C), is equivalent to the charge contained in nearly electrons. (We know that an electron possesses a negative charge of C.) Numerical problems: Example 1. Find the amount of electric charge flowing through the circuit if an electric current of 5 A is drawn by an electric appliance for 5 minute. Solution: Given electric current (I) = 5 A Time (t) = 5 min = 5 X 60 = 300 s Electric charge (Q) =? We know; I = Or, Or, Q = I x t Q = 5 A x 300 s = 1500 C Example 2: If a current of 2 ampere is drawn for 1 hour through the filament of a bulb, find the amount of electric charge flowing through the circuit. Ans: Given electric current (I) = 2 A Time (t) = 1 hour = 1 x 60 x 60 s = 3600 s Electric charge (Q) =? We know that Q = I x t Therefore, Q = 2 x 3600 = 7200 C Electric Potential difference Electric potential difference is known as voltage, which is equal to the work done per unit charge to move the charge between two points.

3 Therefore; Voltage or electric potential difference is denoted by V. Therefore; Where, W = work done Q = Charge. The SI unit of potential difference is volt (V). Definition of one volt 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. Therefore, 1 volt = or 1V = Note: 1.Voltmeter : An apparatus to measure the potential difference between two points in an electric circuit. It is always connected in parallel across the points between which the potential difference is to be measured. Example 3: Calculate the potential difference between two points, if 1500 J of work is done to carry a charge of 50C from one point to other? Ans: Given Work done (W) = 1500J Charge (Q) = 50C Potential difference (V) =? We know that; V = Or, V = = 30 V

4 Symbols used in a Circuit diagram Ohm s Law Ohm's law is the relation between the potential difference applied to the ends of the conductor and current flowing through the conductor. Ohm s law states that at constant temperature the potential difference across the two end of a metallic conductor in an electric circuit is directly proportional to the current flowing through it. Ie, V α I Or, = Constant = R Or, V = IR R is a constant for the given metallic wire at a given temperature and is called its resistance.

5 Resistance: Resistance is the property of conductor which resists the flow of electric current through it. It is equal to the ratio of the potential difference applied across its ends and the current flowing through it. ie, Resistance = or, R = Note: 1. SI Unit of resistance is ohm. Ohm is denoted by Greek letter Ω 2. Definition of 1ohm : If the potential difference across the two ends of a conductor is 1 V and the current through it is 1 A, then the resistance R, of the conductor is 1Ω. That is, 1 ohm = or, 1Ω = 3. V- I graph The graph of V (potential difference) versus I (electric current) is always a straight line. A straight line plot shows that as the current through a wire increases, the potential difference across the wire increases linearly. 4. Variable Resistance: A component used to regulate current without changing the voltage source is called variable resistance. 5. Rheostat : This is a device which is used in a circuit to provide variable resistance, thus to change the resistance in the circuit

6 Factors on which resistance of a conductor depends: The factors on which the resistance of a conductor depends i) Length of the conductor: The resistance of the conductor is directly proportional to its length. Resistance increases with increase in length of the conductor. This is the cause that long electric wires create more resistance to the electric current. ie, Rα l (1) ii) Area of cross section: The resistance of the conductor is inversely proportional to its area of cross section. This means R will decrease with increase in the area of conductor and vice versa. More area of conductor decreases the resistance. This is the cause that thick copper wire creates less resistance to the electric current. ie, R α (2) iii) Nature of the material: resistance of the conductor depends on the nature of which it is made. For example a copper wire has less resistance than a nichrome wire of same length and area of cross-section. iv) Effect of temperature:- Resistance of all pure metals increases on raising the temperature and decreases on lowering the temperature. Resistance of alloys like manganin, nichrome and constantan remains unaffected by temperature. Resistivity Combining eqn (1) and (2) we can write, ie, R α R = ρ (iii) Where ρ (rho) is the constant of proportionality and is called the electrical resistivity of the material of the conductor. From equation (iii) The SI unit of resistivity is Ω m. Note: 1. If l = 1 m, A = 1 m 2 then, eqn (iv) becomes.

7 Resistivity, ρ = R ie, The resistivity of the material is equal to the resistance of the material of unit length and unit area of cross section. 2. Resistivity of the material is independent of the length and area of cross section. It only depends on the nature of the material and its temperature. 3. Electrical resistivity of the material in increasing order Resistivity of Conductors < Resistivity of alloys < Resistivity of insulator RESISTANCE OF A SYSTEM OF RESISTORS The resistances can be combined in two ways 1. In series 2. In parallel To increase the resistance individual resistances are connected in series combination and to decrease the resistance individual resistances are connected in parallel combination. 1. Resistors in Series When two or more resistances are connected end to end then they are said to be connected in series combination. Note: When the resistors are connected in series the current through them remains same but the voltage across them will be different.

8 Consider three resistors of resistance R 1, R 2 and R 3 are connected in series. The potential difference applied across the combination of resistors is V and the current through the circuit is I. Since in series combination current remains same but potential is different so, V = V 1 + V 2 + V (1) If V 1, V 2 and V 3 is the potential difference across each resistor R 1, R 2 and R 3 respectively, then according to Ohm's Law, V 1 =IR 1 V 2 =IR (2) V 3 =IR 3 Substituting eqn (2) in (1) or, V = I R 1 + I R 2 + I R 3 V = I (R 1 + R 2 + R 3 ) (3) Assuming that the three resistors R 1, R 2 and R 3 as a single resistor of resistance R s then, V = IR s (4) Substituting (4) in (3) we get, I R S = I (R 1 + R 2 + R 3 ) ie, R s = R 1 + R 2 + R 3 Thus when the resistors are connected in series, equivalent resistance of the series combination is equal to the sum of individual resistances. For n numbers of resistors connected in series equivalent resistance would be R s = R 1 +R 2 +R R n

9 2. Resistors in parallel. Resistors are said to be in parallel when the ends of the resistors are connected to a common terminal. Note: When the resistors are connected in parallel the voltage across the resistors remains same but the current flowing through each resistor is different. Consider three resistors of resistance R 1, R 2 and R 3 are connected in parallel. The potential difference applied across the combination of resistors is V and the current through the circuit is I. Since in parallel combination voltage remains same but current is different so, I = I 1 + I 2 + I (1) If I 1, I 2 and I 3 is the current through resistor R 1, R 2 and R 3 respectively, then according to Ohm's Law, Substituting the values I 1, I 2 and I 3 in eqn (1) we get (2) Assuming that the three resistors R 1, R 2 and R 3 as a single resistor of resistance R p then, I = ( 3) Substituting eqn (2) and (3) in (1) we get

10 = V Ie, = For resistors connected in parallel combination reciprocal of equivalent resistance is equal to the sum of reciprocal of individual resistances. For n numbers of resistors connected in parallel equivalent resistance would be =

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