The objective of this experiment is to study Kirchoff's Current Law (KCL) and Kirchoff's Voltage Law (KVL) and their application in circuit analysis.

- Multimeter
- DC power supply

In this experiment we will study current and voltage relations in simple networks resulting from the interconnection of two or more simple circuit elements. The elements are assumed to be connected by perfect electrical conductors (zero resistance).

- KCL

We now consider the first of the two laws, KCL, named after Gustov Robert Kirchoff, a German scientist who was born about the same time Ohm was conducting his experiments. Kirchoff's current law states (see Equation 1) that the algebraic sum of all currents entering (see Figure 1) any node is zero. It is evident that KCL can also be stated in other ways. For example, the algebraic sum (see Equation 2) of all the currents leaving a node is zero, or the algebraic sum (see Equation 3) of all the currents leaving a node is equal to algebraic sum of all the currents entering the same node. A general and compact form of the KCL is given in Equation 4.

i_{i}+ i_{2}- i_{3}- i_{4}= 0 (1)

-i_{1}- i_{2}+ i_{3}+ i_{4}= 0 (2)

i_{1}+ i_{2}= i_{3}+ i_{4}(3)

(4)

Note that when Equation 4 is used, it is understood that the N current arrows are all either directed toward the node or directed away from it. - KVL

Kirchoff's voltage law is a very powerful principle that applies to all electrical circuits. KVL states that the algebraic sum (see Equation 5) of the voltages around any closed path (see Figure 2) in a circuit is zero. The KVL can also be stated in other ways. For example, the algebraic sum (see Equation 6) of voltage rises must equal the algebraic sum of the voltage drops. In general KVL can be written as given by Equation 7.

V_{1}- V_{2}+ V_{3}+ V_{4}= 0 (5)

V_{2}= V_{1}+ V_{3}+ V_{4}(6)

(7) - Nodal Analysis

The following summarizes the method by which we may obtain a set of simultaneous equations for any resistive circuit using KCL.- Indicate all element and source values in a neat and simple circuit diagram. Also, mark the reference for each source.
- Provided the network has N nodes, choose one as a reference node. Then label voltages of the remaining (N-1) nodes as V
_{1}, V_{2},...,V_{N-1}. Note that each node voltage is to be measured with respect to the chosen reference. - To obtain the simultaneous equations, for a network with current sources only, apply KCL to each node and order terms from V
_{1}to V_{N-1}. If dependent sources are present, for each source relate the source current and the controlling quantity to variables V_{1}, V_{2},..., V_{N-1}, if they are not already in that form. - If the network contains voltage sources, the circuit is to be temporarily modified, to create a supernode, by replacing each voltage source by a short circuit, thus reducing the number of nodes by one for each voltage source that is present. The assigned node voltages should not be changed. Now apply KCL at the nodes or supernodes. Relate each source voltage to the node voltages V
_{1}, V_{2},...,V_{N-1}, if it is not already in that form.

Before coming to lab preform the following analysis (show your Work in the labbook).

- Using VD = 0.7 V, and KVL find ID, and the marked node voltages for the circuits of Figure 3 and Figure 4.
- Using VD = 0.7 V and KVL find each marked node voltage and element current for Figure 5.
- For the circuit of Figure 6 write the simultaneous equations using KCL and solve for the marked node voltages and element currents.
- For circuit of Figure 7 write the simultaneous equations using KCL and solve for the marked node voltages and element currents.

**Warning: This prelab requires a good deal of time and calculations.**

- Connect circuit of Figure 3 and measure the marked node voltages, and element currents.
- Reverse the diode polarity of the previous circuit and measure all node voltages.
- Connect circuit of Figure 4 and measure the marked node voltages, and element currents.
- Reverse the diode polarity of the previous circuit and measure all node voltages.
- Connect circuit of Figure 5 and measure the marked node voltages, and element currents.
- Reverse the diode polarity of the previous circuit and measure all node voltages.
- Connect circuit of Figure 6 and measure the markedl node voltages, and element currents.
- Connect circuit of Figure 7 and measure the marked node voltages, and element currents.
- Connect circuit of Figure 8 and measure the marked node voltages, and element currents.

Compare (in a table) the measured voltages and currents with the predicted values from the prelab and the values calculate by Pspice in the last lab. Explain any major discrepancies between the three sets of values. What are the advantages and disadvantages of each method?

Is it easier or harder to understand what the answer(s) should look like if you see the simulations first?