IMPLIMENTATION OF RECIPROCITY THEOREM

Understanding what Reciprocity Theorem
Understanding how Reciprocity Theorem work
Implementation of Reciprocity Theorem in a breadboard and simulation
Proving Reciprocity Theorem

1. IMPLIMENTATION OF RECIPROCITY THEOREM

2. Contents of the presentation Objectives introduction Theory Apparatus Circuit Diagram Procedure project model and observations Calculation simulation Result

3. Objectives and outcomes Understanding what Reciprocity Theorem Understanding how Reciprocity Theorem work Implementation of Reciprocity Theorem in a breadboard and simulation Proving Reciprocity Theorem

4. Introduction The principle of reciprocity in acoustic as well as electromagnetic (EM) systems was first enunciated by Lord Rayleigh. Soon afterward, H. A. Lorentz and J. R. Carson extended the concept and provided sound physical and mathematical arguments that underlie the rigorous proof of the reciprocity theorem. Over the years, the theorem has been embellished and extended to cover a broader range of possibilities, and to apply with fewer constraints The basic concept and its proof based on Maxwell’s macroscopic equations are discussed in standard textbooks on electromagnetism. For a recent review of reciprocity in optics, the reader is referred to the comprehensive article by Potton.

5. theory The reciprocity theorem states that  the current at one point in a circuit due to a voltage at a second point is the same as the current at the second point due to the same voltage at the first. The limitation of this theorem is that it is applicable only to single-source networks and not in the multi-source network. The network where reciprocity theorem is applied should be linear and consist of resistors, inductors, capacitors and coupled circuits. The circuit should not have any time-varying elements.

6. In the representative network of Fig. 1(a), the current I due to the voltage source E is determined. If the position of each is interchanged as shown in Fig. 1(b), the current I will be the same value as indicated. To demonstrate the validity of this statement and the reciprocity theorem, consider the network of Fig. 2, in which values for the elements of Fig. 1(a) have been assigned. theory Figure 1(a) Figure 1(b)

7. apparatus Resistor ( 150 Ω , 100 Ω , 100 Ω ) Source ( 9 V ) Breadboard LED Light ( 0.02 A ) Connecting Wire

8. CIRCUIT DIAGRAM Figure : 2(a)

9. Procedure Constructed the circuit as shown in Figure fig 2(a) in a breadboard. Then connected the LED light flowing from terminal C to terminal D keeping the source E between terminal A & B. Moved the source E in between terminals D & C and then connected the LED light flowing from terminal B to terminal A as shown in fig 2(b). Figure : 2(a) Figure : 2 (b)

10. Project model and observations

11. Projects model and observations

12. Projects model and observations

13. Projects model and observations

14. Simulation

15. Simulation

16. calculation At position 1 (When the source is between terminal A and B) : Total resistance, R T = (R 2 ll R 3 )+R 1 = (100 ll 100)+150 = 200 Ω Source current, I T = = = 0.045 A Current through CD terminal, I CD = = = 0.022 A At position 1 (When the source is between terminal A and B) : Total resistance, R T = (R 1 ll R 2 )+R 3 = (150 ll 100)+100 = 160 Ω Source current, I T = = = 0.056 A Current through AB terminal, I AB = = = 0.022 A  

17. Results Error in currents value =  

18. Thank You