Kirchhoff's Laws and Maximum Power Transfer


 Derrick Cannon
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1 German Jordanian University (GJU) Electrical Circuits Laboratory Section Experiment Kirchhoff's Laws and Maximum Power Transfer Post lab Report Mahmood Hisham Shubbak / / 8
2 Objectives: To learn KVL and KCL using the kit and TINA software. To learn how to calculate the maximum power transfer. Introduction and Theory: The Kirchhoff's laws are:. Kirchhoff's current law (KCL): The total current into a node = the total out from it. I. Kirchhoff's voltage law (KVL): The voltage drop through a closed loop = V When we connect an independent voltage or current source in series with a resistor (R S ), the source will deliver the maximum power to a load resistor (R L ) If R L = R S We can calculate the power transferred to any resistor from this equation: P = i.r This experiment consists of two parts: Part : Circuit : Procedure:. Connect the circuit shown in the figure twice: First on TINA simulation software and then on the bread board. Here I used Multisim simulation software instead of TINA.
3 R R.kΩ R.kΩ V V R 7Ω Figure. Measure the theoretical and experimental values of V and I for R, R and R. Results: The theoretical and experimental results of this part are shown in this table: Resistors Theoretical Results Experimental Results % Difference R =. kω %.9% R =. kω % 5.5% R =. kω %.5% This figure shows the flow of current through the circuit and the instantaneous voltage and current in some important points. R I:.9 ma V:.5 V I:.9 ma I: 7.6 ma V V I:. ma R.kΩ V:.9 V I:. ma V:.9 V I:. ma R V:.9 V I:.99 ma R.kΩ V:.5 V I:.99 ma V:.5 V I: 5.9 ma 7Ω V: V I: 7.6 ma V: V I:. ma V: V I: 5.9 ma % difference T E T %
4 This circuit can be simplified using to Y transformation: I:.9 ma R V:.5 V I:.9 ma Ra 6Ω V:. V I:.9 ma I: 7.6 ma I:. ma V V R.kΩ V:.9 V I:. ma Rb 68Ω V:. V I:. ma V:. V I: 7.6 ma Rc 67Ω V: V I: 7.6 ma Circuit : Procedure:. Connect the circuit shown in the figure also twice: First on TINA simulation software and then on the bread board. R V V R kω R 7Ω R kω Figure. Measure the theoretical and experimental values of V and I for R, R and R.. Simplify the circuit. Results: The theoretical and experimental results of this part are shown in this table: Resistors Theoretical Results Experimental Results % Difference R =. kω %.55% R =. kω %.888% R = kω % 8.% Here I used Multisim simulation software instead of TINA.
5 This figure below shows the flow of current through the circuits and the instantaneous voltage and current in some important points. I:.8 ma V V I:. ma I:.8 ma R kω V:.57 V R I:.8 ma V:.57 V I: 9 ua R V:.57 V I:. ma 7Ω V: V I:.8 ma V: V I:. ma V: V I: 9 ua R kω V: 9 mv I: 9 ua V: 9 mv I: 9 ua V: V I:. ma We can redraw this circuit in a better way as shown in this figure below. R V V R kω R 7Ω R kω Part : Procedure:. Connect the circuit shown in the figure on the bread board. R kω V 5 V R kω R 7Ω Figure. Change the value of R as shown in the table (in the Manual).. Measure V across R in each time.. Draw a table of results then plot the (voltage power) resistance relationship to find the maximum power transfer. 5
6 Results: The results of this part are shown in this table: R (kω) V V measured %Difference.7.8. %...5 % % When we plot the (voltage power) resistance relationship we get the graph shown below..5 & Power P (mwatt) V P Resistance of R (KΩ) This graph was drawn according to the simulation values as shown in the table below. R (kω) V P (mwatt) Discussion In this experiment we had % difference in the values of V, I and R, this might be because one of these reasons:. The resistance of wires used to make the circuits.. The resistance of the used resistors was slightly less than its theoretical value.. Systematic errors. 6
7 Conclusion We can calculate the values of and (I) for any simple circuit using the Kirchhoff's laws:. Kirchhoff's current law: the total current into the node = the total out from.. Kirchhoff's voltage law: the voltage drop through a closed loop = When we connect an independent voltage or current source in series with a resistor (R S ), the source will deliver the maximum power to a load resistor (R L ) If R L = R S The maximum power transfer can be calculated from this equation: P max = V TH / R L In the second part of this experiment the maximum power transferred to R: P max =.7 mwatt when R = Ω 97
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