Electrical Current and Ohm’s Law BASIC DATA ABOUT ATOM : Mass of electron = 9.11 x 10-31 kg Mass of proton = 1.67 x 10-27 kg Mass of neutron = mass of proton Mass of electron = 1/1840 mass of proton Diameter of nucleus is of the order of 10-14 m Diameter of orbits = 104 times dia of molecule Diameter of electron = 10-15 m Charge on electron = - 1.602 x 10-19 coulomb Charge on proton = + 1.602 x 10-19 coulomb. UNIT OF CURRENT : The charge on an electron is measured in terms of coulomb. The unit of current is coulomb per second and is called ampere.Thus I (Ampere) = coulomb/second = ∆ q / ∆ t One coulomb is equivalent to the charge of 6.28 x 1018 electrons. RESISTANCE : Resistance is the property of a substance due to which it opposes the flow of electrons (i.e., electric current) through it. The unit of resistance is ohm (Ω). Metals, acids and salt solutions are good conductors of electricity. Silver, copper and aluminium offer least resistance to flow of current and are called very good conductor of electricity. The electrons while flowing through the molecules or the atoms of the conductor, collide with other atoms and electrons, thereby producing heat. Some substances offer relatively greater difficulty or hindrance to the passage of these electrons. Such substances are called poor conductors or insulators of electricity. Some of the insulators are glass, bakelite, mica, rubber, polyvinyl chloride (P.V.C.), dry wood, etc. The resistance of a conductor depends on: 1. Length of conductor- it varies directly with the length 1 2. Cross-sectional area of the conductor - it varies inversely with the cross-sectional area 3. Its resistivity i.e. the nature of composition, etc., of the material of which the conductor is made up 4. Temperature of the conductor - it almost varies directly with the temperature. Thus R, the resistance of a conductor is given by R=ρl/A where ρ = specific resistance or resistivity of the material, l = length of the conductors, A = cross-sectional area of conductor. OHM's LAW : If the temperature and other conditions remain constant, the current through a conductor is proportional to the applied potential difference and it remains constant. Thus Current = Applied Voltage / Resistance of the circuit Resistance = Applied voltage / Current in the circuit Potential across resistance = Current x Resistance. Conditions for Ohm's Law : 1. Ohm's law can be applied either to the entire circuit or a part of a circuit. 2. When ohm's law is applied to a part circuit, part resistance and the potential across the part resistance should be used. 3. The Ohm's law can be applied to DC as well as AC circuits. However, in case of AC circuits impedance Z, is used in place of resistance. Thus I = E / Z = Applied voltage / Impedance in the circuit Conductance (G ) : Conductance is the reciprocal of ( R ) and is measure of the ease with which the current will flow through a substance. Thus G= 1 / R The unit of conductance is mho. 2 ELECTRICAL POWER : Electrical power is expressed in terms of watts (W) and is given by W= E x I = I2 x R = E2 / R Power is also expressed in terms of kW ( kilowatt ) ( =1000 W ) or MW ( megawatt ) which is 1000 kW or 1000,000 W. Electrical Energy : Electrical energy is expressed in terms of kilowatt hours (kWh). Thus 1 kWh = 1 kW x 1 hour = 1000 watt-hours = 1000 x 60 x 60 watt-sec. RESISTANCE COMBINATIONS : Resistances in series : When resistances are connected in series, same current flows through all resistances, and overall resistance R, is given by R = R1 + R2 + R3 Also, V = V1 + V2 + V3 = IR1+ IR2 + IR3 . Resistances in Parallel : When 3 conductors are joined in parallel, following relations hold good I = I1 + I2 + I3 1 / R= 1 / R1 + 1 / R2 + 1 / R3 R= ( R1+R2 + R3 ) / ( R1R2 + R2R3 + R3R1 ) G = G1 + G2 + G3 Effect of Temperature on Resistance : Resistance of all materials is affected by the variations in temperature. The effect of temperature in general is as follows: (i) Resistance of most of the metallic conductors increases with rising temperature (ii) Resistance of non-conductors or insulators usually decreases with rising temperature. Resistor color coding : Carbon resistors are physically small in size and color code is used to represent their value in ohms. The scheme is shown in Figure above. Various codes for colors are given in the table below : Color Code Color Black Brown Red Orange Yellow Green Blue Violet Grey White Value 0 1 2 3 4 5 6 7 8 9 4 5