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Mastering Network Theorems: Kirchhoff, Thevenin, Superposition

Understand Kirchhoff's laws, source conversion, Thevenin's theorem, Superposition theorem, and more. Practice simple problems and grasp Delta/star transformations. Learn how to apply voltage and current laws in circuits effectively.

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Mastering Network Theorems: Kirchhoff, Thevenin, Superposition

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  1. CHAPTER-2 NETWORK THEOREMS

  2. CONTENT 1. Kirchhoff’s laws, voltage sources and current sources. 2. Source conversion, simple problems in source conversion. 3. Superposition theorem, simple problems in super position theorem. 4. Thevenin’s theorem, Norton’s theorem, simple problems. 5.Reciprocity theorem, Maximum power transfer theorem, simple problems. 6. Delta/star and star/delta transformation.

  3. Gustav Robert Kirchhoff

  4. Definitions • Circuit – It is an interconnection of electrical elements in a closed path by conductors(wires). • Node – Any point where two or more circuit elements are connected together • Branch –A circuit element between two nodes • Loop – A collection of branches that form a closed path returning to the same node without going through any other nodes or branches twice

  5. Example • How many nodes, branches & loops? R1 + Vo - Is + - Vs R2 R3

  6. Example-Answer • Three nodes R1 + Vo - Is + - Vs R2 R3

  7. Example-Answer • 5 Branches R1 + Vo - Is + - Vs R2 R3

  8. Example-Answer • Three Loops, if starting at node A A B R1 + Vo - Is + - Vs R2 R3 C

  9. Example 9 How many nodes, branches & loops? 5 5

  10. Kirchhoff's Current Law (KCL) Also called Kirchhoff's Point law and Kirchhoff's First rule..

  11. Kirchhoff's Current Law (KCL) Total volume of water flowing through pipe 1 = (total volume of water flowing through pipe 2 + total volume of water flowing through pipe 3)

  12. Kirchhoff's Current Law (KCL) Total current entering the node through the wire 1 = (total current leaving the node through the wire 2 + total current leaving the node through the wire 3)

  13. Kirchhoff's Current Law (KCL) "The algebraic sum of all currents entering and leaving a node must equal zero" ∑ (Entering Currents) = ∑ (Leaving Currents) Established in 1847 by Gustav R. Kirchhoff

  14. Kirchhoff's Current Law (KCL) It states that, in any linear network the algebraic sum of the current meeting at a point (junction) is zero. ∑ I (Junction) = 0

  15. Kirchhoff's Current Law (KCL) ∑ I (Entering) = ∑ I (Leaving) ∑ I (Entering) - ∑ I (Leaving) =0

  16. Kirchhoff's Current Law (KCL) Assign positivesigns to the currents entering the node and negativesigns to the currents leaving the node, the KCL can be re-formulated as: S (All currents at the node) = 0

  17. Kirchhoff's Current Law (KCL)

  18. Kirchhoff's Current Law (KCL)

  19. Kirchhoff's Current Law (KCL)

  20. Example I1= 1 A I2= 3 A I3= 0.5 A Find the current I4 in A

  21. Kirchhoff's Voltage Law (KVL) Also called Kirchhoff's loop rule and Kirchhoff's second rule..

  22. Kirchhoff's Voltage Law (KVL) “The algebraic sum of voltages around each loop is zero”. Σ voltage rise - Σ voltage drop = 0 Or Σ voltage rise = Σ voltage drop

  23. Kirchhoff's Voltage Law (KVL) It states that, in any linear bilateral active closed network the algebraic sum of the product of the current and resistance in each of the conductors in any closed path (mesh) in the network plus the algebraic sum of e.m.f in the path is zero. ∑ IR + ∑ e.m.f = 0

  24. Kirchhoff's Voltage Law (KVL)

  25. Sign Convention The sign of each voltage is the polarity of the terminal first encountered in traveling around the loop. The direction of travel is arbitrary. Clockwise: Counter-clockwise:

  26. Example • Kirchoff’s Voltage Law around 1st Loop A I1 + I1R1 - B R1 + Vo - I2 + I2R2 - Is + - Vs R2 R3 C Assign current variables and directions Use Ohm’s law to assign voltages and polarities consistent with passive devices (current enters at the + side)

  27. Example • Kirchoff’s Voltage Law around 1st Loop A I1 + I1R1 - B R1 + Vo - I2 + I2R2 - Is + - Vs R2 R3 C Starting at node A, add the 1st voltage drop: + I1R1

  28. Example • Kirchoff’s Voltage Law around 1st Loop A I1 + I1R1 - B R1 + Vo - I2 + I2R2 - Is + - Vs R2 R3 C Add the voltage drop from B to C through R2: + I1R1 + I2R2

  29. Example • Kirchoff’s Voltage Law around 1st Loop A I1 + I1R1 - B R1 + Vo - I2 + I2R2 - Is + - Vs R2 R3 C Subtract the voltage rise from C to A through Vs: + I1R1 + I2R2 – Vs = 0 Notice that the sign of each term matches the polarity encountered 1st

  30. Source Conversion

  31. Voltage Source to Current Source

  32. Current Source to Voltage Source

  33. Proof

  34. Convert to Current Source

  35. Answer-1

  36. Convert to Voltage Source

  37. Answer-2

  38. Superposition Theorem STATEMENT- In a network of linear resistances containing more than one generator (or source of e.m.f.), the current which flows at any point is the sum of all the currents which would flow at that point if each generator were considered separately and all the other generators replaced for the time being by resistances equal to their internal resistances.

  39. Superposition Theorem STATEMENT- In a linear circuit with several sources the voltage and current responses in any branch is the algebraic sum of the voltage and current responses due to each source acting independently with all other sources replaced by their internal impedance.

  40. Superposition Theorem Replace a voltage source with a short circuit.

  41. Superposition Theorem Replace a current source with an open circuit.

  42. Superposition Theorem Step-1: Select a single source acting alone. Short the other voltage source and open the current sources, if internal impedances are not known. If known, replace them by their internal resistances.

  43. Superposition Theorem Step-2: Find the current through or the voltage across the required element, due to the source under consideration, using a suitable network simplification technique.

  44. Superposition Theorem Step-3: Repeat the above two steps far all sources.

  45. Superposition Theorem Step-4: Add all the individual effects produced by individual sources, to obtain the total current in or voltage across the element.

  46. Explanation

  47. Superposition Theorem Consider a network, having two voltage sources V1 and V2. Let us calculate, the current in branch A-B of network, using superposition theorem. Step-1: According to Superposition theorem, consider each source independently. Let source V1 is acting independently. At this time, other sources must be replaced by internal resistances.

  48. Superposition Theorem But as internal impedance of V2 is not given, the source V2 must be replaced by short circuit. Hence circuit becomes, as shown. Using any of the network reduction techniques, obtain the current through branch A-B i.e. IAB due to source V1 alone.

  49. Superposition Theorem Step 2: Now Consider Source V2 volts alone, with V1 replaced by short circuit, to obtain the current through branch A-B. Hence circuit becomes, as shown. Using any of the network reduction techniques, obtain the current through branch A-B i.e. IAB due to source V2 alone.

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