1 / 27

Network Theorems

Network Theorems. Circuit analysis. Mesh analysis Nodal analysis Superposition Thevenin’s Theorem Norton’s Theorem Delta-star transformation. Application of Kirchoff’s law in network analysis. Direct application in conjunction with Ohm’s law

sheppards
Download Presentation

Network Theorems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Network Theorems

  2. Circuit analysis • Mesh analysis • Nodal analysis • Superposition • Thevenin’s Theorem • Norton’s Theorem • Delta-star transformation

  3. Application of Kirchoff’s law in network analysis • Direct application in conjunction with Ohm’s law • Indirect application in conjunction with resistance • Simultaneous equations

  4. Example 1 Determine current and source e.m.f Since R3 and R4 are in parallel Therefore Also By Kirchoff’s first law By Kirchoff’s second law

  5. Example 2 Determine I1, E, I3 and I By Kirchoff’s second law Also By Kirchoff’s first law

  6. Example 3 Power dissipated in R3 is 20W. Calculate I3, R1,I1, I2 and E a b 3 1 2 d c By Kirchoff’s first law in node a By Kirchoff’s first law in node b P.D across 1 W is 5 X 1=5V By Kirchoff’s second law in loop 2

  7. Example 4 Determine current I and I4 First find the total effective resistance Then Using current division

  8. Example 5 Determine VAB Effective resistance for parallel resistor 10W // 15 W and 16W//16W Using voltage division Then

  9. Example 6 Calculate the current in each resistor Applying Kirchoff’s 2nd law for loop 1 ---(a) Applying Kirchoff’s 2nd law for loop 2 ---(b) But Thus ---(b)

  10. continue Solving the 2 simultaneous equations ---(c) (a) X 4 (b) X 7 ---(d) Then (c) + (d) In 3W resistor Substitute in (b) In 8W resistor In 28W resistor In 14 W resistor In 4 W resistor

  11. Example 7 Calculate the current in the network Applying Kirchoff’s 2nd law for loop 1 ---(a) Applying Kirchoff’s 2nd law for loop 2 Substitute I1 in(a) ---(b) ---(c) (a)x10 Current in 18 W resistor ---(d) (b)X 9 (d)-(c) we get

  12. Example 8 Calculate the current in the network Applying Kirchoff’s 2nd law for loop 2 Current in 18 W resistor Applying Kirchoff’s 2nd law for outside loop Current in 1 W resistor

  13. Example 9 The network shown is a 3 cells having an internal resistance of 30 W. Calculate the current in the network Applying Kirchoff’s 2nd law The voltage drop due to internal resistor is 0.05 x30=1.5V Thus there is no potential different between two terminals

  14. Mesh analysis • Create loop’s current rather than branch current • Use Kirchoff’s second (voltage ) law • Ohm’s law to calculate p.d • Branch is calculated by taking the algebraic sum of the loop currents

  15. Example 10 Calculate the current in each branch First create loop current ,i.e I1 , I2, I3 as shown

  16. continue In loop 1 ---(a) In loop 2 ---(b) In loop 3 ---(c)

  17. continue Solving these equations In direction of I1 Current in 60W Current in 30W In direction of I1 Current in 50W In direction of I2 Current in 40W In direction of I2 In direction of I2 Current in 10W Current in 20W In direction of I3

  18. Nodal analysis • Choose reference node where all nodes can refer • Assign currents going to/out the nodes • Assign voltage at nodes as V1 , V2, V3….which refer to reference node • Apply Kirchoff’s current law at each node • Relate the voltage , resistance andcurrent using ohm’s law • Solve the equations obtained

  19. Example 11 Calculate V1 and V2 At node 1 Simplified ….(a) At node 2

  20. continue Simplified …..(b) Solve for equations (a) and (b) (b) X 21 (a) X 15 Substitute V2 we have

  21. Example 12 Calculate V1 and V2 and current in 8W At node 1 Simplified ….(a)

  22. continue At node 2 Simplified ….(b) Solving the simultaneous equations (a) and (b)

  23. Superposition The superposition states that in any network containing more than one source , the current in , or the p.d. across in any branch can be found by considering each source separately and adding their effects: omitted sources of e.m.f are replaced by resistance equal to their internal resistances.

  24. Separating the network into several circuit contenting only one source Original network Separating into 2 networks

  25. Network 1 Total resistance Thus and Also

  26. Network 2 Total resistance Thus and Also

  27. combination Thus and Also

More Related