Answer Happy

3. Is the fact that the Norton’s theorem is based on the concept
of a constant current generator likely to limit its usage? Why?
4. What facts deduced from the results of this test indicate
whether the theorems have been verified or not?
5. Plot the curve of the power against the load resistance and
determine the maximum power.
Experiment 5 Thevenin's and Norton's Theorem & Maximum Power Transfer 5.1 Objective The objective of this experiment is to understand how to analyze a circuit using Thevenin's Theorem in a circuit, also the relation between Thevenin and Norton Theorems. Another aim is to investigate the circuit requirements for the transfer of maximum power from the power source to the load. 5.2 Equipment Breadboard sbon Resistors (R=2, R2=3,3ko, R3-6800, R=1000, Rs=1000, R380, RTH = ?) Resistors (R=3,3ko, R.(POT)=10kn) Power Supply Multimeter 5.3 Theory Thevenin's and Norton's Theorem Thevenin and Norton equivalents are circuit simplification techniques that focus on terminal behavior and thus are extremely valuable aids in analysis. There is a Thevenin equivalent circuit in Figure 5.1. The latters a and b denote the pair of terminals of interest. Thus, a Thevenin equivalent circuit is an independent voltage source Vt in series with a resistor Rth, which replaces an interconnection of sources and resistors. This series combination of VH and Rthis equivalent to the original circuit in the sense that, if we connect the same load across the terminals a,b of each circuit, we get the same voltage and current at the terminals of the load. RTH . a VTH ob Figure 5.1 Thevenin equivalent circuit Isc = VTH RTH A Norton equivalent circuit consists of an independent current source in parallel with the Norton equivalent resistance. We can derive it from a Thevenin equivalent circuit simply by making a source transformation. Thus the Norton current equals the short-circuit current at the terminals of interest, and the Norton resistance is identical to the Thevenin resistance. Maximum Power Transfer Maximum power transfer can best be described with the aid of the circuit shown in Figure 5.1. We assume a resistive network containing independent and dependent sources and a designated pair of terminals, a,b, to which a load, R , is to be connected. The problem is determine the value of Rthat permits maximum power delivery to R. The first step in this process is to recognize that a resistive network can always be replaced by its Thevenin equivalent greatly simplifies the task of finding R 1
RE=RTH VZRL Vin Prax = (2R) 4RL 5.4 Preliminary Work son w A 400V 200Ω {Ri B Figure 5.2 1. For the given circuit in Figure 5.2, find the open circuit voltage Vry and the short circuit current In across the terminal. 2. For the same circuit, find RH by using the RTV/In equation and find Rt with replacing voltage source with short circuit. 3. Let's assume we connect RL (load resistance) to the circuit between points A and B, what should be the value of Re in order to have max power transfer. 4. Why do we need maximum power transfer? Explain. 5.5 Procedure Thevenin's and Norton's Theorem 1. Set up the circuit in Figure 5.3. Do not turn on the supply. 2. Using the resistors color code, find the resistor values for the given resistors. 3. Calculate the In, and RH from Figure 5.3. 4. Remove resistor R from the network. 5. Turn on the supply. Measure the voltage between the points A and D of the network. This is the Thevenin's voltage. Record the value in Table 5.1. 6. Then measure short-circuit current across A and D terminals. Note that this current is the short circuit current (Isc) and it is equal to I Norton current. Fill these values in the Table 5.1. OSS 7. Switch off the power supply. Replace the power supply with a short circuit. S 8. Measure the resistance between terminals A and D. This is the Thevenin's resistance (at the same time it is the Norton's resistance) Record the value in Table 5.1. 9. Place back the resistor R, in circuit with an ammeter is connected between terminals A and B or C and D. 10. Remove the short circuit connection and place back the supply in the circuit. 11. Turn on the supply. Read and record the current value flowing in the resistor R. 12. Compare the measured and calculated values for VTH, Rth, and IN. 13. Draw Thevenin's equivalent circuit inclusive of resistor RL 14. Draw Norton's equivalent circuit inclusive of resistor RL. 15. Set up this Thevenin's equivalent circuit inclusive of resistor R. (Figure 5.4) 16. Measure the current (U) flowing through the circuit in Figure 6.4. Compare li with the current flowing through resistor R in the circuit Figure 5.3. 2,20mA 2
RS A =R: & akn SR 12V D Figure 5.3 RTH SR Figure 5.4 Thevenin equivalent circuit Maximum Power Transfer 17. Connect the circuit shown in Figure 5.5 below. From the circuit, we can note that R=3,3K ohm and V=12V. 18. Change the value of RL in steps as shown in Table 5.2. 19. Measure the voltage "V" and current "I" and record them in Table 5.2. 20. Plot the value of the power with respect to the value of the load resistor R. 3,3ко w IL A) VLV SRL 12V Figure 5.5 5.6 Results 1. Plot an exact curve of PL vs. RL. Explain the curve in the Lab. Report. (Thevenin's and Norton's Theorem part) 2. Fill in your results in Table 5.2.
Table 5.1 Measured Values circuit Thevenin Resistance (RTHERN) Thevenin Voltage Short current (Isc=IN) Calculated Values 0 289 Al Thevenin Short circuit Thevenin Current in RL Resistance current Voltage (RTHERN) (Isc=IN) 3.24v 0.0057 A AN Current in RL 10.5686683.234 0.0055A 2.86 mA 0.568k Table 5.2 1000 1500 2000 3000 3300 4000 4500 5500 7000 RL (0) 500 (mA) 3.16 V (volt) 1.71 Power S.40 11.81 6.03 11.17 8.19 9,5 110.91