# Kirchhoff's laws

DC Experiment 5

In this section we study two important laws in circuits: Kirchhoff's Current Law (KCL) and Kirchhoff’s Voltage Law (KVL). Kirchhoff’s laws are essentially the energy conservation theorem applied in circuits.

Kirchhoff’s Current Law

Kirchhoff’s Voltage Law

It is important to first understand the concept of nodes in a circuit. When multiple elements are connected at a point, this point is called a node. In Figure 5.1 we labeled points a, b and c, but technically speaking b is the only node of concern since it is attached to three elements. The bottom point is also a node but more often referred as a ground.

Kirchhoff’s Current Law, or KCL states that the net current of a node is always equals to 0. On the circuit diagram it means at node b the algebraic sum of I1, I2 and I3 is zero.

The three currents on the diagram are arbitrarily assigned, and from the equation we noticed currents can be positive or negative, this is only to do with the definition of current directions. For example, if we set current flowing into the node as positive, then I2 will be negative since it is flowing out. If I2 was drawn on the opposite direction, then we put a positive sign as well.

To apply Kirchhoff’s Voltage Law (KVL), we need to understand the definition of a loop, which is defined as a closed path in a circuit. The circuit drawn in Figure 5.2 has three loops.

KVL states that for any loop in a circuit, the algebraic sum of all voltages equals to 0. According to the law, we can write the loop equations for all three loops specified in the circuit. Note that the voltage polarities are determined based on your arbitrarily assigned loop orientations.

Kirchhoff’s laws are fundamental concepts in circuits and can be used to solve complex circuit problems. In this tutorial, the goal is to understand the basic concepts of Kirchhoff’s laws from an experimental perspective, and no significant calculations are involved in this section.

**Part I: Verifying KVL**

- 1.Build the circuit as shown in Figure 5.3. Use R1 = R3 = R4 =1.0 kΩ, R2 = 3.3 kΩ. Set power supply to 6V.

- 2.Starting with voltage measurements in Loop a. Please note that the multimeter should be connected to match the polarities labeled in the diagram, refer to Figure 5.4 for setup.

- 3.Substitute your measured results for VS, VR1 and VR2 into the loop an equation, do they add up to 0?

- 4.We now continue for loop b. Follow the measurement setup in Figure 5.5. Note that the polarity of the multi-meter should be consistent to the polarity labeled in diagram.

- 5.Substitute your measured results for VR2, VR3 and VR4 into the loop b equation, do they sum up to 0? Note that your measured VR2 could be negative.

**Part II: Verifying KCL**

- 1.This part will verify that the three currents at node b sums up to 0. We use the same current directions assigned in Figure 5.6. All resistors and power supply voltage remain the same as in Part I.

- 2.Measure current I1, I2 and I3 as the way shown in Figure 5.7. Setup ammeter in the same direction as the currents assigned in the diagram.

The current are measured one at the time, and each time other two branches need to connect and only one is opened to place the ammeter.

- 3.Substitute your measured results for I1, I2 and I3 into the KCL equation at node b, do they sum up to 0?

- 1.Write the KVL equation for loop c. Draw the circuit below and label the polarities of the voltages in the loop.
- 2.If you got a negative result on the multi-meter while measuring the voltage or current, what does it indicate for the actual voltage polarity or current direction?