Experiment No. 5 Kirchhoff's Rules Presented by Group 2 Introduction Gustav Robert Kirchhoff (1824-1887) Kirchhoff's Current Law Kirchhoff's Voltage Law "The algebraic sum of all the potential differences around any loop in a circuit is equal to zero." Gustav Robert Kirchhoff, a physicist who made important contributions to the theory of circuits using topology and to elasticity. Kirchhoff's laws allow calculation of currents, voltages, and resistances of electrical circuits extending the work of Ohm. To experimentally demonstrate Kirchhoff's rules for electrical circuits. To prove clearly the two rules of Kirchhoff's, namely, the KCL and the KVL. Objectives Digital Multimeter Two D-Cell Batteries Converter Resistors Wire Leads Circuits Experiment Board Materials and Apparatus Procedure 1. Connect the circuit shown in Figure 7.1a using any of the resistors except the 100 ohm. Use Figure 7.1b as a reference along with 7.1a as you record your data. Record the resistance values on the table below. With no current flowing (the battery disconnected), measure the total resistance of the circuit between points A and B. 1 3 2. With the circuit connected to the battery and the current flowing, measure the voltage across each of the resistors and record the values in the table below. On the circuit diagram in Figure 7.1b, indicate which side of each resistors is positive relative to the other end by placing a '+' at the end. 3. Now measure the current through each of the resistors. Interrupt the circuit and place the DMM in series to obtain your reading. Make sure you record each of the individual currents, as well as the currents, as well as the current flow into or out of the main part of the circuit, I . 2 Figure 7.1b Figure 7.1a t Resistance, Voltage, Volts Current, mA R 46.8 R R R R R 147.7 47.1 148.9 328 97.6 V V V V V V 0.89 2.75 0.87 2.73 0.02 3.63 I I I I I I 0.03 0.08 0.03 0.08 0 0.02 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 T T T Table 7.1 Analysis of Results A. Questions 1. Determine the net current flow into or out of each of the four "nodes" in the circuit. 2. Determine the net voltage drop around at least three (3) of the six or so closed loops. Remember, if the potential goes up, treat the voltage drop as positive (+), while if the potential goes down, treat it as negative (-). B. Answers 2. The sum of all the voltage drops around the loop is equal to zero as stated by Kirchhoff's Voltage law. Theory Observations 1. Resistors having almost the same resistance also have potential differences similar with each other. is almost the same with , same as with and . 2. is equal to and

is equal to . 1. Since and , also and , are connected in parallel, their voltage is the same. 2. In a parallel connection, the value of the current passing through a resistor must not be necessarily the same. It depends upon the value of the resistor. If the value of the resistor is the same, then the current across it is the same. Conclusion I I I I 1 2 3 4 V 5 Simple circuits can be analyzed using Ohm’s law and the rules for series and parallel combination of resistors. Very often it is not possible to reduce a complex circuit to a single loop. Therefore, to analyze complex circuits, we may use Kirchhoff’s law. We can simplify complicated circuits using of Kirchhoff's rules, the Current law and the Voltage law. But before introducing the rules we need to deﬁne the technical meanings of a junction and a loop.

Junction (Branch point) refers to any point where three

or more circuit elements meet.

Loop refers to any closed path of a circuit such that the point you start with is also the point you end up with. "The algebraic sum of all the currents entering and leaving any branch point in a circuit is equal to zero." This is based on the principle of conservation of energy. This is based on the principle of the law of conservation of charge. in out 1. The sum of currents entering a node is equal to the sum of currents leaving the same node I =I so the net ﬂow of electrical current into or out of a node is zero as indicated by Kirchhoff's Current law. Current entering a point in a circuit is equal to the current leaving the same point. The potential rise and potential drop within a specific closed circuit in a network must be equal. V V V V 1 2 3 4 R R R R 1 2 3 4 I 5 3. is almost zero and is exactly zero. Interpretation 3. Using the measured current values, Kirchhoff's Current law was applied separately to each node. The sum of the currents entering the node should equal the sum of the currents leaving the node. For each node, the percent difference is computed between the sum of the currents into the node and the sum of the currents out of the node.

Using Kirchhoff's Voltage law, the sum of the changes in electric potential is zero for any loop in the circuit. For each loop, the percent difference was computed between the sum of the potential rise and the sum of the potential drop in the loop. An electrical circuit called the Wheatstone Bridge was used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. This was used to experimentally demonstrate Kirchhoff's rules. Using the values measured from the Wheatstone Bridge circuit, it was proven that the algebraic sum of the currents at any junction of an electric circuit is equal to zero ,which states Kirchhoff's Current law, and the algebraic sum of all emf's and the resistance voltages in any continuous path of an electric circuit is equal to zero, which states Kirchhoff's Voltage law. In a complex circuit, the algebraic sum of the currents at any junction of an electric circuit is equal to zero, and the algebraic sum of all emf's and the resistance voltages in any continuous path of an electrical circuit is also equal to zero.

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# Kirchhoff's rules

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