DC Circuits PDF

Circuit Elements Electric Charge and Current  The most basic quantity in an electric circuit is the electric charge.  We all experience the effect of electric charge when we try to remove our wool sweater and have it stick to our body or walk across a carpet and receive a shock. Charge is an...

Circuit Elements Electric Charge and Current  The most basic quantity in an electric circuit is the electric charge.  We all experience the effect of electric charge when we try to remove our wool sweater and have it stick to our body or walk across a carpet and receive a shock. Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C). 2 Circuit Elements What is an electric circuit?  It is a closed path for transmitting an electric current through the medium of electrical and magnetic fields.  The flow of electrons across the loop constitutes the electric current.  Electrons enter the circuit through the ‘Source’ which can be a battery or a generator. 4 Circuit Elements  Passive Element: The element which receives energy (or absorbs energy) and then either converts it into heat (R) or stored it in an electric (C) or magnetic (L ) field is called passive element. 7 Circuit Elements: Resistor Resistance (R)  Resistance is a “property” of material which opposes the flow of electricity through it when potential is applied. 14  From ohm’s law  V1 = 2 x i V2 = 3 x i _____________(1)  Applying KVL around the loop gives  20 - V1 - V2 = 0 _________________(2)  Substituting Eq.(1) into Eq.(2)  20 - 2 i– 3 i = 0 or 5 i = 20 therefore, i = 4 A.  Substituting I in Eq.(1) finally gives  V1 = 2 x i = 8 V and V2 = 3 x i = 12 V. Kirchhoff’s Laws Observations from the Circuit Junction: A & D Loop: ABDA & ACDBA Current follows the Ohm’s law 54  We will apply Ohm’s Law and Kirchhoff’s Laws. By Ohm’s Law,  V1 = 8 x I1 V2 = 3 x I2 V3 = 6 x I3  Applying KCL at node a,  i1 – i2 – i3 =0 _______________(1)  Applying KVL to Loop 1,  30 – V1 – V2 = 0 _______________(2)  We express Eq.(2) in terms of i1 and i2  30 – ( 8 x I1) – (3 x I2 ) = 0________(3)  Therefore, i1 = [30 – (3 x I2 )] / 8  30 – 3 I2 – 8 i2 – 4 i2 = 0  30 – 15 I2 = 0  Which gives the value of I2 = 2 A.  From the value of I2 the value of i1 = [30 – (3 x I2 )] / 8 = 3 A and I3 = I2 /2 =1 A.  V1 = 8 x I1 = 24 V,  V2 = 3 x I2 = 6 V,  V3 = 6 x I3 = 6 V. 58 Kirchhoff’s Laws Example-3: Find the branch currents. Consider the source voltage 200 V. 59 Kirchhoff’s Laws Example-4: Find the branch currents. Consider the source voltage 50 kV. 61 Electromagnetism 79 Electromagnetism Magnetic Field: Electromagnet  Here, Magnetism exists only when current flows through the coil/winding placed on a magnetic material. Controllable magnetic field can be created. 82 Electromagnetism Laws of Magnetic Force (Coulomb’s Laws)  First Law: Like poles repel each other while unlike poles attract each other. Charles Coulomb 83 Electromagnetism Observe the direction of pointer of the galvanometer when motion of the magnet is reversed. 88 Electromagnetism  As current through A is changed, the flux linked with B is also changed.  Hence, mutually induced emf is produced in B whose magnitude is given by Faraday’s Laws and direction by Lenz’s Law. Mutually Induced emf (DC) 102 Electromagnetism  Hence, it is also known as the opposing or counter or back emf of self-induction. Current Variable Resistor Self-induced emf supplied emf by battery Magnetic field 105 Electrostatics 117 Electrostatics Coulomb’s Laws of Electrostatics Like charges Unlike charges 121 Electrostatics Force exerted on water due to charged balloon Force exerted on sphere due to another sphere 122 Electrostatics  A parallel-plate capacitor is shown in figure. A B  One plate is joined to the positive end of the supply and the other to the negative end or is earthed.  When such a capacitor is put across a battery, there is a momentary flow of electrons from A to B. 129 DC Response of RC Circuit Vs C Charging & Discharging of Capacitor R 153