ELECTRICITY Electric Current Conventional Current Electric Circuit Electric Potential and Potential Difference Symbols used in Circuit Diagram 6. Ohm’s Law 7. Resistance and Resistivity 8. Conductance and Conductivity Series and Parallel combination of resistors Heating Effect of Current Joule’s Law of Heating Electric Power and Electric Energy Electric Fuse

Electric Current The electric current is defined as the charge flowing through any section of the conductor in one second. I = Q t (if the rate of flow of charge is steady) Different types of current: Steady current which does not vary with time b I t c a b) & c) Varying current whose magnitude varies with time d d) Alternating current whose magnitude varies continuously and direction changes periodically

SI unit of electric charge is coulomb (C) and SI unit of time is second (s). SI unit of electric current is coulomb / second or C/s. (From the formula) Or SI unit of electric current is ampere (A). (Named after the French scientist, Andre-Marie Ampere (1775 – 1836)) Note: Q = ne ( Q – charge, n – no. of electrons and e – electronic charge) Charge of one electron is 1.6 x 10-19 coulomb. 1 coulomb is equivalent to the charge of 6.25 x 1018 electrons. 1 coulomb, in fact, is very high charge. Therefore, charge is expressed in smaller units like milli coulomb (mc) or micro coulomb (µC). Similarly current is expressed in milli ampere (mA) or micro ampere (µA).

Conventional Current Conventional current is the current whose direction is along the direction of the motion of positive charge under the action of electric field. ++++ - - - - + I ++++ - - - - Conventional current due to motion of electrons is in the direction opposite to that of motion of electrons. - I

Electric Circuit A continuous and closed path of an electric current is called an electric circuit. A simple electric circuit consists of a cell (or battery), switch (or key) and load (or resistance). An ammeter (current measuring instrument) is always connected in series in an electric circuit. A voltmeter (potential measuring instrument) is always connected in parallel (shunt) across the load (or resistance). V I R I I I A E E K K An Electric Circuit with Ammeter and Voltmeter A Simple Electric Circuit

Electric Potential Electric potential is a physical quantity which determines the flow of charges from one body to another. It is a physical quantity that determines the degree of electrification of a body. Electric Potential at a point in the electric field is defined as the work done in moving (without any acceleration) a unit positive charge from infinity to that point against the electrostatic force irrespective of the path followed. V = W Q SI unit of electric potential is volt (V) or J C-1 or Nm C-1. (named after Alessandro Volta (1745-1827), an Italian Physicist) Electric potential at a point is one volt if one joule of work is done in moving one coulomb charge from infinity to that point in the electric field.

Electric Potential Difference Electric Potential Difference between any two points in the electric field is defined as the work done in moving (without any acceleration) a unit positive charge from one point to the other against the electrostatic force irrespective of the path followed. WAB Q VB - VA = ∆V = Electric potential and potential difference are scalar quantities. Electric potential at infinity is zero. Electric potential near an isolated positive charge (q > 0) is positive and that near an isolated negative charge (q < 0) is negative. cgs unit of electric potential is stat volt. 1 stat volt = 1 erg / stat coulomb

Ohm’s Law Ohm’s Law Experiment The electric current flowing through a conductor is directly proportional to the potential difference across the two ends of the conductor when physical conditions such as temperature, mechanical strain, etc. remain the same. I I α V or V α I or V = R I E Ohm’s Law Experiment I V R E A K I V Graph is linear (straight line)

Resistance in terms of physical features of the conductor The resistance of conductor is the opposition offered by the conductor to the flow of electric current through it. R = V I Resistance in terms of physical features of the conductor where ρ is proportionality constant called ‘ resistivity’ or ‘specific resistance’, l is the length of the conductor and A is the area of cross section of the conductor. A R = ρ l Resistance is directly proportional to length and inversely proportional to cross-sectional area of the conductor and depends on nature of material. Resistivity depends upon nature of material and not on the geometrical dimensions of the conductor. Both the resistance and resistivity vary with temperature.

Conductance and conductivity SI unit of resistance is ‘ohm’ and its symbol is ‘Ω’. 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 of the conductor is said to be 1 ohm. SI unit of resistivitiy is ‘ohm-m’ or Ωm. Conductance and conductivity Conductance is the reciprocal of resistance. Its S.I unit is mho. Conductivity is the reciprocal of resistivity. Its S.I unit is mho / m.

Resistance of a system of resistors Resistors in series R1 R2 R3 I I Resistors are said to be in series combination when they are connected end to end. V1 V2 V3 I I I I In series combination, Current through each resistor is same. A - + K V 2. Potential difference across resistors of unequal resistance is different. However, the total p.d. is the sum of the p.d. across the individual resistors. V = V1 + V2 + V3 IR = IR1 + IR2 + IR3 Or R = R1 + R2 + R3 The Effective or Equivalent Resistance of the resistors in a series combination is the sum of the resistances of the individual resistors. Note: The Effective or Equivalent Resistance of the resistors in a series combination is greater than the greatest of them.

Resistors in parallel V R1 Resistors are said to be in parallel combination when they are connected together between two points. I1 I2 R2 I I I3 R3 I I In parallel combination, Potential difference across each resistor is same. I I A - + K V 2. Current through resistors of unequal resistance is different. However, the total current supplied by the battery is the sum of the currents through the individual resistors. The reciprocal of Effective or Equivalent Resistance of the resistors in a parallel combination is the sum of the reciprocals of resistances of the individual resistors. I = I1 + I2 + I3 = V R + R1 R3 R2 Note: The Effective or Equivalent Resistance of the resistors in a parallel combination is smaller than the smallest of them. = 1 R + R1 R3 R2 Or

HEATING EFFECT OF CURRENT Joule’s Law: When an electric current is passed through a conducting wire, the electrical energy is converted into heat energy. This effect is called ‘heating effect of electric current’. It is also called ‘Joule Heating’. Joule’s Law gives Q = I2 R t Q is in Joule, I in Amp, R in ohm and t in sec. I2 R t J Q = Q is in Calorie, I in Amp, R in ohm and t in sec. Cause of Heating Effect of Current: When a battery is connected to the ends of a conductor, electric field is set up. The free electrons move in the direction opposite to the field. They undergo collision with the positive ions and atoms of the conductor. The average kinetic energy of vibration of the ions and the atoms increases and hence the temperature increases. Note: The course of electron through resistor is like that of the stone falling in water.

Electric Power Electric Energy Electric power is the rate at which work is done by an electric current. P = V I P = I2 R P = V2 / R SI unit of power is ‘watt’. Other units are ‘kW’ and ‘hp’. 1 kW = 1000 W 1 hp = 746 W Electric Energy Electric energy is the total work done by an electric current in a given time. E = V I t E = I2 R t E = V2 t / R Commercial Unit of Electric Energy is kWh or B.O.T.U. 1 kWh = 1000 w x 3600 s = 3600000 w-s or joule = 3.6 x 106 joule

Electric Fuse Electric fuse is a protective device used in series with an electric circuit or an electric appliance to save it from damage due to overheating produced by strong current in the circuit or appliance. Fuse is generally made of alloy of 63% tin and 37% lead. It has high resistance and low melting point. Electric Heating Appliances use Nichrome wire (alloy of Ni and Cr). It is used because: It has high specific resistance ii) It has high melting point iii) It has high malleability iv) It is not easily oxidised. For given V, P α I P α 1 / R i.e. i) Higher the power of the appliance, more is the current drawn ii) Higher the power of the appliance, less is the resistance.