Fundamental Concepts in Electrical Engineering
Lab2 - Kirchhoff’s Voltage and Current Laws
Objectives

- Learn Kirchhoff's Voltage Law
- Learn Kirchhoff's Current Law
- Apply Kirchhoff's Voltage Law to the analysis of a series circuit
- Apply Kirchhoff's Current Law to the analysis of a parallel circuit

Components

- Resistors: 1Ohm (1%, 0.25W) 3 pieces,100Ohms (10%, 0.5W), 560Ohms(10%,0.5W), 820Ohms(10%, 0.5W)
- Circuit prototyping breadboard
- Electric wires

Equipment

- Adjustable power supply (at least 0 - 5V voltage range, and 0.5A maximum current)
- Tektronix TBS 1202B-EDU Oscilloscope

Theory
1. Kirchhoff’s Voltage Law
Kirchhoff’s voltage law describes the relationship between the voltage sources and voltage drops on loads in a circuit loop. A simple example is shown in the following figure. According to Kirchhoff’s voltage law the algebraic sum of voltages in a loop is equal to zero. Notice the polarities of voltages on the battery and the three resistors. In red it is shown the direction of electric current as flowing from the positive terminal of the battery through the three resistors and back into the battery. The voltage on the battery has polarity opposite to the direction of electric current and therefore it is algebraically added as negative value.
In the example above we knew the direction of electric current; however, there are often cases when we do not know the direction of electric current through the circuit loop. To apply Kirchhoff’s voltage law we don’t really need to know the actual direction of electric current; we can just define an arbitrary direction and write Kirchhoff’s voltage for that direction. This is exemplified in the figure below:
In this example we defined an arbitrary direction through the loop, clockwise in the example 1 and counter-clockwise in example 2. Notice that the Kirchhoff’s voltage laws written for these two opposite arbitrary directions result in the same equation.
To further clarify the Kirchhoff’s voltage law let’s look at the following example, which includes multiple voltage sources and connected with reverse polarities.
So depending on the arbitrary direction chosen, some supply voltages are summed with a positive sign and others with a negative sign.
2. Kirchhoff’s Current Law
Kirchhoff’s current law describes quantitatively the relationship between the intensity of electric currents that flow in and out of a circuit node. From an intuitive perspective, by looking at the figure below we can deduce that as I_total current splits into three currents, I1, I2, and I3, the number of charges of I_total that flow through the wire in a unit of time would have to split among the three paths of I1, I2, and I3. So if we combine the number of charges that flow in one second in I1, I2, and I3 currents the sum should be equal to I_total’s number of charges that flow in one second (no charges are lost and no charges are created). This is exactly what Kirchhoff’s current law states, that:
I_total = I1 + I2 + I3,
or in the general form: the algebraic sum of electric currents flowing into a circuit node is equal to zero.
How does the current split? How much would it go through one resistor and how much through the others? Let's look at an example: R1 = 1kOhms, R2= 3kOhms and R3 = 9kOhms, all connected in parallel to a 9V voltage supply. Applying Ohm’s law to each resistor, V=I1*R1, V=I2*R2, and V=I3*R3, we know V and R1, R2, R3, so we can calculate the value of each current: I1=9mA, I2=3mA, and I3=1mA.
Experimental Setup
Part 1: Kirchhoff's Voltage Law
Construct the circuit shown in the diagram below and continue with the steps listed in the "Procedure" section.
Part 2: Kirchhoff's Current Law
Construct the circuit shown in the diagram below and continue with the corresponding steps listed in the "Procedure" section.
In this circuit the 1Ohm 1% resistor is used as a current to voltage converter with the transfer function: 1A -> 1V, 100mA -> 100mV, 10mA -> 10mV,... This way we can use one channel of the oscilloscope to probe the current through the circuit.