Fig. 1 - R1 = 2.2 kW, R2 = 1.8 kW, R3 = 3.3 kW
OBJECTIVES:
1. To study the characteristic of a linear circuit.
2. To apply the superposition principle to a linear circuit.
BACKGROUND & THEORY:
A linear circuit is composed entirely of independent sources, linear dependent sources, and linear elements.
A linear dependent source has an output which is proportional to the first power of some voltage or current in the circuit.
A linear circuit element is one which has a linear voltage-current relationship.
The superposition principle is expressed as follows:
In any linear circuit containing several sources, the voltage across (or current through) any circuit element may be obtained by adding algebraically the individual voltages (or currents) caused by each independent source acting alone, with the other independent voltages killed (voltage sources replaced by short circuits and current sources replaced by open circuits).
EQUIPMENT AND PARTS LIST:
Power Supply.
Digital Multimeter (DMM).
Resistors: 1.8
kW,
2.2 kW, 3.3 kW
Breadboard.
PROCEDURE:
1. Measure the resistor values and construct the circuit shown in Figure 1.
Fig. 1 - R1 = 2.2 kW, R2 = 1.8 kW, R3 = 3.3 kW
2. Set the three outputs of the power supply to provide +10, +5, and -10 volts. Then measure and record the actual values of each supply output with the DMM.
3. With V2 = 0 (jumper wire connected from node 2 to ground--instead of a power supply terminal), use V1 = +10 volts and measure V3'. Then repeat for V1 = +5 volts, and V1 = -10 volts.
4. With V1 = 0 (jumper wire connected from node 1 to ground--instead of a power supply terminal), use V2 = +10 volts and measure V3". The repeat for V2 = +5 volts, and V2 = -10 volts.
5. With V1 = +10 volts, measure V3 for each of these values of V2: +10 volts (you will have to use a second jumper wire to get the voltage at both terminals), +5 volts, and -10 volts.
6. Repeat 5 for V1 = +5 volts.
7. Repeat 5 for V1 = -10 volts.
CALCULATIONS, COMPARISONS, & QUESTIONS:
A possible format for presenting the results of the calculations below is shown by this link.
1. Calculate the theoretical value of V3' using the measured resistor values with V2 = 0 and for V1 = +15 volts, +6 volts, and -10 volts. Then plot V3' versus V1. On the same graph plot the experimental or measured values of V3' versus V1. Plot the experimental data points with a small symbol (, x, or 0) at each point. Do not connect these experimental data points with lines. Plot the theoretical points with no symbols connected by a line. Use a spreadsheet to plot the graph.
2. Calculate the theoretical value of V3" using the measured resistor values with V1 = 0, and for V2 = +10 volts, +5 volts, and -10 volts. Then plot V3" versus V2 similar to plot under 1 above, but on separate graph. Also show experimental or measured values.
3. From 1 and 2 above, make a statement about linearity. Are V3' and V3" linear functions of V1 and V2 respectively?
4. Calculate all the values of V3 for all combinations of voltages used using the measured values of the source voltages and resistors. (you may use superposition for this) and list in the attached form.
5. Calculate V3 = (V3' + V3") from the measured values of V3' and V3" and list the results on the attached format.
6. Calculate and fill in the % difference tables
7. Using calculated data from 1 and 2 above, calculate V3
for the circumstances of V1 and V2 having the same
voltages of + 10 volts, +5 volts, and - 10 volts. Then make the following
comparisons:
| Theoretical V3 | Measured V3 | |
| V1 = V2 = 10 V | ||
| V1 = V2 = 5 V | ||
| V1 = V2 = -10 V |
CONCLUSIONS:
What have you learned about linearity and the superposition principle?
Last updated 02/19/2008