Network Analysis VTU scheme all theorems
- 2. Module-2 • Network Theorems: Superposition, Millman's theorems, Thevenin's and Norton’s theorems, Maximum Power transfer theorem
- 3. Superposition theorem • The principle of superposition is applicable only for linear systems. • In any linear circuit containing multiple independent sources, the current or voltage at any point in the network may be calculated as algebraic sum of the individual contributions of each source acting alone.
- 4. • Action Plan: • (i) In a circuit comprising of many independent sources, only one source is allowed to be active • in the circuit, the rest are deactivated (turned off). • (ii) To deactivate a voltage source, replace it with a short circuit, and to deactivate a current • source, replace it with an open circuit. • (iii) The response obtained by applying each source, one at a time, are then added algebraically • to obtain a solution.
- 5. • Find the current in the 6 Ω resistor using the principle of superposition for the circuit
- 6. • Find io in the network shown using superposition.
- 9. • Use superposition to find io in the circuit shown
- 11. • Find the current i for the circuit.
- 15. Find vx • 5.33V
- 17. • Find the voltage V1 using the superposition principle
- 19. Thevenin’s theorem • Reducing the circuit
- 20. Thevenin’s theorem • “A linear two–terminal circuit can be replaced by an equivalent circuit consisting of a voltage source Vt in series with a resistor Rt, Where Vt is the open–circuit voltage at the terminals and Rt is the input or equivalent resistance at the terminals when the independent sources are turned off or Rt is the ratio of open–circuit voltage to the short–circuit current at the terminal pair.”
- 21. Action plan for using Thevenin’s theorem • Divide the original circuit into circuit and circuit . • Separate the circuit from circuit • Replace circuit A with its Thevenin’s equivalent. • Reconnect circuit and determine the variable of interest
- 22. Procedure for finding Rt 1.If the circuit contains only independent sources and resistors, deactivate the sources and find Rt by circuit reduction technique. Independent current sources, are deactivated by opening them while independent voltage sources are deactivated by shorting them. 2.If the circuit contains resistors, dependent and independent sources, follow the instructions described below: (a) Determine the open circuit voltage Voc with the sources activated. (b) Find the short circuit current ioc when a short circuit is applied to the terminals: Rt=Voc/ioc
- 23. 3. If the circuit contains resistors and only dependent sources, then (a) Voc= 0 (since there is no energy source) (b) Connect 1A current source to terminals a-b and determine vab. (c) Rt=Voc/1
- 24. Using the Thevenin’s theorem, find the current i through = 2Ω.
- 29. Find the Thevenin equivalent for the circuit with respect to terminals a-b .
- 34. The wheatstone bridge in the circuit shown in Fig. is balanced when R2 = 1200 Ω. If the galvanometer has a resistance of 30 Ω, how much current will be detected by it when the bridge is unbalanced by setting R2 to 1204 Ω ?
- 35. Millman’s theorem • Millman’s theorem states that if n number of generators having generated emfs E1, E2 …. E and internal impedances Z1,Z2,….. Z are connected in parallel, then the emfs and impedances can be combined to give a single equivalent emf of E with an internal impedance of equivalent value Z.
- 38. • Find the current through 10 Ω resistor using Millman’s theorem.
- 40. • Find the current through (10 -j 3)Ω using Millman’s theorem.
- 42. • Refer the circuit shown .Use Millman’s theorem to find the current through (5+5j) Ω impedance.
- 43. Find the current through 2 ohm resistor.
- 44. Norton’s theorem • Norton’s theorem states that a linear two-terminal network can be replaced by an equivalent circuit consisting of a current source iN in parallel with resistor RN, where iN is the short-circuit current through the terminals and RN is the input or equivalent resistance at the terminals when the independent sources are turned off. • If one does not wish to turn off the independent sources, then RN is the ratio of open circuit voltage to short–circuit current at the terminal pair.
- 45. Procedure for finding Norton’s equivalent circuit: (1) If the network contains resistors and independent sources, follow the instructions below: (a) Deactivate the sources and find RN by circuit reduction techniques. (b) Find iN with sources activated. (2) If the network contains resistors, independent and dependent sources, follow the steps given below: (a) Determine the short-circuit current iN with all sources activated. (b) Find the open-circuit voltage voc
- 46. Find the Norton equivalent for the circuit
- 47. Find the value of ib using Norton equivalent circuit. Take R= 667 Ω.
- 50. Find I0 using Norton’s theorem
- 56. Maximum power transfer theorem • The maximum power transfer theorem states that the maximum power delivered by a source represented by its Thevenin equivalent circuit is attained when the load RL is equal to the Thevenin resistance Rt .
- 59. Find the load that will result in maximum power delivered to the load for the circuit and also find the maximum power transferred
- 61. Find the load that will result in maximum power delivered to the load for the circuit and also find the maximum power transferred
- 62. Maximum power transfer theorem in AC circuit The linear circuit is made up of impedances, independent and dependent sources. This linear circuit is replaced by its Thevenin equivalent circuit as shown. In rectangular form, the Thevenin impedance Zand the load impedance Zare In rectangular form, the Thevenin impedance Zt and the load impedance ZL are
- 63. The current through the load is The phasors I and V are the maximum values. The corresponding RMS values are obtained by dividing the maximum values by square root of 2. Also, the RMS value of phasor current flowing in the load must be taken for computing the average power delivered to the load. The average power delivered to the load is given by P=1/2(|I|2R) P
- 64. we can conclude that for maximum average power transfer, ZL must be selected such that XL = - Xt and RL=Rt That is the maximum average power of a circuit with an impedance Ztthat is obtained when ZL is set equal to complex conjugate of Zt.
- 65. we get the maximum average power as
- 66. H.W • Apply Superposition theorem and find I
- 67. Obtain the Norton’s equivalent of the network
- 68. • Calculate the current through the galvanometer for the Kelvin double bridge shown in Fig.. Use Thevenin’s theorem. Take the resistance of the galvanometer as 30 Ω.
- 69. Find the Thevenin and Norton equivalent circuits in frequency domain
- 72. Find I using Millman’s Theorem on AC circuits