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Electrical Engineering & Control Systems (15EE232) Ravi Chaurasia Ph. -09411826365 [email protected] Notes of lessons UNIT-I ELECTRIC CIRCUITS (DC CIRCUITS) Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance,[1] one arrives at the usual mathematical equation that describes this relationship: Where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current. Voltage Division v1 R1i R1 v total R1 R2 R3 v2 R2 i R2 v total R1 R2 R3 Electrical Engineering & Control Systems (15EE232) Ravi Chaurasia Ph. -09411826365 [email protected] Current Division Rule i1 R2 v itotal R1 R1 R2 i2 R1 v itotal R2 R1 R2 KIRCHOFF’S LAW: A German physicist Gustav Kirchhoff developed two laws enabling easier analysis of circuit containing interconnected impedances. The first law deals with flow of current and is known as Kirchhoff ‘s Current Law (KCL) while the second one deals with voltage drop in a closed circuit and is known as Kirchhoff ‘s Voltage Law (KVL). KIRCHHOFF ‘S CURRENT LAW (KCL): It states that in any electric network the algebraic sum of currents meeting at any node of circuit is zero. This low is based on Conservation of charge. n i (t ) 0 j 1 j KIRCHOFFS VOLTAGE LAW (KVL) : It states that the algebraic sum of voltages in any closed path, in a network traveled in a single direction is zero. This low is based on conservation of energy. Electrical Engineering & Control Systems (15EE232) Ravi Chaurasia Ph. -09411826365 [email protected] n v (t ) 0 j 1 j SUPERPOSITION THEOREM Statement: In a linear bilateral network containing several sources, the current through or voltage across any branch in the network equals the algebraic sum of the currents or voltage of each individual source considered separately with all other sources replaced by resistance equal to the internal resistances. Or The response of a circuit to more than one source can be determined by analyzing the circuit’s response to each source (alone) and then combining the results Analyze Separately, then Combine Results Electrical Engineering & Control Systems (15EE232) Ravi Chaurasia Ph. -09411826365 [email protected] For deactivation of sources Current source is zero – open circuit as I = 0 and solve iX Voltage source is zero – short circuit as V= 0 and solve iXv i X i Xv i Xc THEVENINS THEOREM Statement; The current flowing through a load resistance connected across any two terminals A and B of linear bilateral network is given by V oc/R i+R L. Where Voc is open circuit voltage RI is the internal resistance as viewed from the open terminals. Or Any resistive circuit or network, no matter how complex, can be presented as a voltage source in series with a source resistance Electrical Engineering & Control Systems (15EE232) Ravi Chaurasia Ph. -09411826365 [email protected] Thevenin Resistance (RTH) – the resistance measured across the output terminals with the load removed Steps 1-Determine the open-circuit voltage Vt = voc. 2-Zero the sources and find the Thévenins resistance Rt looking back into the terminals 3-The Thévenin equivalent consists of a voltage source Vt in series with Rt . Thévenins Equivalent Circuits Electrical Engineering & Control Systems (15EE232) Ravi Chaurasia Ph. -09411826365 [email protected] NEELKANTH INSTITUTE OF TECHNOLOGY, MEERUT Department of Electrical and Electronics Engineering Lecture Notes – 10 NORTONS THEOREM Statement -Any resistive circuit or network, no matter how complex, can be represented as a current source in parallel with a source resistance Nortons Theorem Any resistive circuit or network, no matter how complex, can be presented as a current source in parallel with a source resistance.Or According to this theorem any two terminal active network containing voltage sources and resistance when viewed from its output terminal is equivalent to a constant current source and an internal resistance in parallel Norton Current (IN) – the current through the shorted load terminals Electrical Engineering & Control Systems (15EE232) Ravi Chaurasia Ph. -09411826365 [email protected] For Calculating Isc or In Norton Resistance (RN) – The resistance measured across the open load terminals (measured and calculated exactly like RTH) Norton-to-Thevenin and Thevenin-to-Norton Conversions Electrical Engineering & Control Systems (15EE232) Ravi Chaurasia Ph. -09411826365 [email protected] Steps -1. Determine the short-circuit current In = isc. 2. Use the equation Vt = Rt In to compute the remaining value. 3. The Norton equivalent consists of a current source In in parallel with Rt . Electrical Engineering & Control Systems (15EE232) Ravi Chaurasia Ph. -09411826365 [email protected] Maximum Power Transfer Theorem A resistive load withdraws maximum power from the circuit when the value of load resistance equals the internal resistance of the network as viewed from the output terminals, with all energy sources removed leaving behind the internal resistance. Or The load resistance that absorbs the maximum power from a two-terminal circuit is equal to the Thévenin resistance