ECE 170 Lab #2 Voltage and Current Division
Lab #2 Voltage and Current Division
In this experiment, we will be investigating the concepts of voltage and current division. Voltage and current division is an application of Kirchoff’s Laws.
Kirchoff’s Voltage Law
Kirchoff’s Voltage Law (KVL) states that the sum of all voltage drops around any loop in any circuit sum to zero. In mathematical form,
Where the vi in Equation (2.1) are the voltages across the individual components in any circuit. As an example of how to use Kirchoff’s Voltage Law to solve a circuit, consider the circuit shown in Figure 2.1.
If we apply Equation (2.1) to the loop contained in the left half of Figure (2.1), and then the right half of the circuit, while traversing each loop in a clockwise direction, we obtain the two equations
This approach produces two equations for which there are three unknowns. We could use the equation for the outer loop Figure 2.1 to obtain a system of three equations and three unknowns. This would work, but there is an easier way. Let us do away with all the voltages shown in Figure 2.1 except the source and define currents flowing in the two main loops. This is shown in Figure 2.2. Since we are defining the currents, we are free to choose their directions. Call the currents I1 and I2.
Let us now write equations by applying Kirchoff’s Voltage Law for the left and right loops as before, but using our defined currents. Each loop is traversed in the clockwise direction.
We now have two equations with two unknowns that can easily be solved. To obtain the voltages as shown in Figure 2.1, just use Ohm’s Law. These voltages are given as
Solving a circuit by defining your own currents allows you to configure the currents that would provide an easy solution. Once these are obtained, any quantity desired can be solved for. Also, by defining your own currents, you will make fewer mistakes, as it is easier to keep track of polarities of components in your equations.
Kirchoff’s Current Law
Kirchoff’s Current Law (KCL) is similar to his voltage law. It states that all currents entering or leaving any circuit node (connection point) sum to zero. Mathematically, this is
To solve a circuit with Kirchoff’s Current Law, consider the circuit shown in Figure 2.3 where we have arbitrarily chosen the currents as I1, I2, and I3.
Applying Equation (2.2) at the node symbolized by Vx,
We can then substitute for the currents using Ohm’s Law. This yields,
Thus we now have one equation with one unknown (Vx). This allows us to easily solve the circuit and obtain any circuit voltage or current desired.
Equivalent Resistance
Consider the circuit shown in Figure 2.4.
Since the resistors have the same current flowing through them, by Ohm’s Law
Where
Thus, we can conclude the equivalent resistance of any number of resistors in series is the sum of the resistances.
For resistors in parallel, consider the circuit shown in Figure 2.5.
By Kirchoff’s Current Law,
The formula for the equivalent resistance of resistors in parallel that is given above can be extended to any number of resistors by adding another term to the denominator. If two resistors are in parallel, this formula can be reduced to a much more convenient form. Simplifying, the equivalent resistance of two resistors in parallel is given by
Instructional Objectives
2.1 Take voltage readings at various points in a circuit.
2.2 Take current readings at various points in a circuit.
2.3 Explain the operation and function of a potentiometer.
2.4 Identify and verify voltage and current division configurations in a circuit.
2.5 Verify Kirchoff’s Laws.
Procedure
1. Adjust the DC power supply to output 10V. Obtain two 10kW resistors and one 27kW resistor as shown in Figure 2.6. Measure the actual values of these resistors and the power supplies voltage. Record your data in Table 2.1. Be sure to keep track of resistors and not mix them up since you have measured their values.
Vs ______
2. Measure the voltages as shown in Figure 2.6 and record their values in Table 2.1.
Component/Value / Nominal R Value
(kW) / Measured
R Value
(kW) / Measured Voltage
(V) / Calculated Voltage
(Pre-Lab)
(V)
R1, V1
R2, V2R3, V3
Table 2.1: Measured Data for Figure 2.6.
3. Using your measured values for R1, R2, R3, and Vs, calculate the voltage drops for V1, V2, and V3. Place these in the “Actual Calculated Volts” column in Table 2.2. Calculate the % error of your measured voltages to the pre-lab voltages (data in Table 2.1) using the pre-lab values as the accepted values. Also calculate the % error of your “actual calculated values” to the measured values (from Table 2.1). Use the measured values as the accepted values in your calculations. Place these results in Table 2.2.
Component/Value / Actual
Calculated
Volts
(V) / % Error
Calculated to
Measured / % Error
Actual Calculated to
Measured
R1, V1
R2, V2R3, V3
Table 2.2: Calculated Data and Errors for Figure 2.6.
4. The errors you obtained in Table 2.2 should be less than 5%. If they are not, try to find the reason why.
5. Construct the circuit shown in Figure 2.7. Measure the actual value of the supply voltage and the values of the resistors you use.
Vs ______
6. Repeat steps 2 and 3 for the currents I1, I2, and I3. Record your data in Tables 2.3 and 2.4. Always turn off power when you are making changes in the circuit, such as moving the ammeter to measure a different current.
Component/Value / Nominal R Value
(kW) / Measured
R Value
(kW) / Measured Current
(mA) / Calculated Current
(Pre-Lab)
(mA)
R1, I1
R2, I2R3, I3
Table 2.3: Measured Data for Figure 2.7.
Component/Value / Actual
Calculated
Amps
(mA) / % Error
Calculated to
Measured / % Error
Actual Calculated to
Measured
R1, I1
R2, I2R3, I3
Table 2.4: Calculated Data and Errors for Figure 2.7.
7. In this part of the experiment, we will be investigating the properties of the potentiometer. The potentiometer is a variable resistor. A functional representation of a potentiometer is shown in Figure 2.8. Measure the resistance between the upper and lower terminals of the potentiometer. Record this value. Also record what happens to the measured resistance as you rotate the shaft of the device. Record what happens to the resistance between the wiper and the upper terminal and the wiper and lower terminal as the shaft of the pot is rotated.
8. Construct the circuit shown in Figure 2.9. Adjust the potentiometer until Vout is 1V. Record the value of Vs and Vout.
Vs ______Vout ______
9. Shut off the power and disconnect the power supply from the circuit. Carefully, without moving the arm of the potentiometer, measure the resistance between the upper and center terminal and then between the lower and center terminal. Record these values.
Rupper-center ______Rlower-center ______
10. This is a design problem. Your task is to design a circuit that will deliver 1.5V ± 5% across a load resistor of 10kW. Figure 2.10 demonstrates the problem. The resistors available for use are listed in Figure 2.10. As with most engineering design problems, there are constraints. In this case, your design must cost less than 20 cents. Each resistor costs 6 cents. Assume your time is free. Design and document a circuit that will meet the design criteria. Record your proposed solutions and brainstorm until you have found a solution. Construct your proposed circuit. Verify that it meets the design criteria by measuring Vin and Vout. When your circuit is working, demonstrate the design to the lab instructor. You may use more than one resistor of a particular value if you wish.
Vin ______Vout ______
Post Lab Questions
2.1. Draw a schematic diagram similar to Figure 2.6 except label the elements with the measured resistance and computed voltage. Compare the voltages you calculated to the voltages you measured for the circuit in Figure 2.6. Explain why they may not be exactly equal. Verify that Kirchoff’s Voltage Law applies to this circuit using your measured values.
2.2 Compare the currents you calculated to the currents you measured for Figure 2.7. Explain why they may not be exactly equal. Verify that Kirchoff’s Current Law applies to this circuit.
2.3 For the potentiometer circuit of step 8 and 9, draw the equivalent voltage divider circuit and label the resistances with their actual measured values. Use the measured values and the voltage divider relationship to show that the potentiometer functions as a voltage divider.
2.4 Draw the circuit you designed in step 10. Explain the reasoning you used to get to your final solution and discuss how you verified that the circuit met the design criteria.
2.5 Assume that the supply voltage was exactly 5V and the resistors were ideal in step 10. For what range of Rload will your circuit deliver 1.5V ± 5%? In other words, what is the maximum and minimum resistance of Rload for which the circuit will still operate?
Name: ______Section: ______
Pre-Lab #3: Linearity, Proportionality, and Superposition
1. For the circuit shown in Figure 3.0a, calculate the proportionality constant that relates the output voltage to the input voltage, k=Vout/Vin.
2. Calculate the voltages V5V and V15V as shown in Figures 3.0b and 3.0c respectively.
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