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ELECTRIC CIRCUIT ANALYSIS - I

ELECTRIC CIRCUIT ANALYSIS - I. Chapter 8 – Methods of Analysis Lecture 11 by Moeen Ghiyas. TODAY’S lesson. CHAPTER 8. TODAY’S LESSON CONTENTS. Bridge Networks Y – Δ (T – π ) and Δ to Y ( π – T) Conversions. Bridge Networks. A configuration that has a multitude of applications

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ELECTRIC CIRCUIT ANALYSIS - I

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  1. ELECTRIC CIRCUIT ANALYSIS - I Chapter 8 – Methods of Analysis Lecture 11 by MoeenGhiyas

  2. TODAY’S lesson CHAPTER 8

  3. TODAY’S LESSON CONTENTS • Bridge Networks • Y – Δ (T – π) and Δ to Y (π – T) Conversions

  4. Bridge Networks • A configuration that has a multitude of applications • DC meters & AC meters • Rectifying circuits (for converting a varying signal to one of a steady nature such as dc) • Wheatstone bridge (smoke detector ) and other applications • A bridge network may appear in one of the three forms

  5. Bridge Networks • The network of Fig (c) is also called a symmetrical lattice network if R2 = R3 and R1 = R4. • Figure (c) is an excellent example of how a planar network can be made to appear non-planar

  6. Bridge Networks (Standard Bridge Configuration) • Solution by Mesh Analysis (Format Approach)

  7. Bridge Networks • Solution by Nodal Analysis (Format Approach) Can we replace R5 with a short circuit here?

  8. Bridge Networks • Can we replace R5 with a short circuit? • Since V5 = 0V, yes! From nodal analysis we can insert a short in place of the bridge arm without affecting the network behaviour • Lets determine VR4 and VR3 to confirm validity of short ie VR4 must equal VR3 As before VR4 and VR3 = 2.667 V

  9. Bridge Networks • Can we replace same R5 with a open circuit? • From mesh analysis we know I5 = 0A, therefore yes! we can have an open circuit in place of the bridge arm without affecting the network behaviour (Certainly I = V/R = 0/(∞ ) = 0 A) • Lets determine VR4 and VR3 to confirm validity of open circuit ie VR4 must equal VR3

  10. Bridge Networks (Balancing Criteria) • The bridge network is said to be balanced when the condition of I = 0 A or V = 0 V exists • Lets derive relationship for bridge network meeting condition I = 0 and V = 0

  11. Bridge Networks (Balancing Criteria) • If V = 0 (short cct b/w node a and b), then V1 = V2 or I1R1 = I2R2

  12. Wheatstone Bridge Smoke Detector

  13. Y – Δ (T – π) and Δ to Y (π – T) Conversions • Two circuit configurations not falling into series or parallel configuration and making it difficult to solve without the mesh or nodal analysis are Y and Δ or (T and π). • Under these conditions, it may be necessary to convert the circuit from one form to another to solve for any unknown qtys • Note that the pi (π) is actually an inverted delta (Δ)

  14. Y – Δ (T – π) and Δ to Y (π – T) Conversions • Conversion will normally help to solve a network by using simple techniques • With terminals a, b, and c held fast, if the wye (Y) configuration were desired instead of the inverted delta (Δ) configuration, all that would be necessary is a direct application of the equations, which we will derive now • If the two circuits are to be equivalent, the total resistance between any two terminals must be the same

  15. Y – Δ (T – π) and Δ to Y (π – T) Conversions • If the two circuits are to be equivalent, the total resistance between any two terminals must be the same • Consider terminals a-c in the Δ -Y configurations of Fig

  16. Δ to Y (π – T) Conversions • If the resistance is to be the same between terminals a-c, then To convert the Δ (RA, RB, RC) to Y (R1, R2, R3)

  17. Δ to Y (π – T) Conversions

  18. Δ to Y (π – T) Conversions Note that each resistor of the Y is equal to the product of the resistors in the two closest branches of the Δ divided by the sum of the resistors in the Δ.

  19. Y to Δ (T – π) Conversions

  20. Y to Δ (T – π) Conversions

  21. Y to Δ (T – π) Conversions Note that the value of each resistor of the Δ is equal to the sum of the possible product combinations of the resistances of the Y divided by the resistance of the Y farthest from the resistor to be determined

  22. Y – Δ (T – π) and Δ to Y (π – T) Conversions • what would occur if all the values of a Δ or Y were the same. If RA = RB = RC

  23. Y – Δ (T – π) and Δ to Y (π – T) Conversions • The Y and the Δ will often appear as shown in Fig. They are then referred to as a tee (T) and a pi (π) network, respectively

  24. Y – Δ (T – π) and Δ to Y (π – T) Conversions • Example – Find the total resistance of the network

  25. Summary / Conclusion • Bridge Networks • Y – Δ (T – π) and Δ to Y (π – T) Conversions

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