Department of Electronics and Mechanical Date:
ELEC 195 - Circuits Theory II
Experiment 3
The Natural Response of an RC Circuit
Objective:
- To become familiar with the natural response of an RC circuit.
- To become familiar to Agilent VEE software
- To compare the mathematical expression of the voltage across the capacitor with the experimental data obtained via Agilent VEE
Equipment Required:
Resistors: 2 X100 k
Capacitors:100F
Leads:2 pairs of banana to alligators clips
Jumpers
A breadboard
Resume of Theory:
The natural response of an RC circuit is developed from the circuit shown below. We begin by assuming that the switch has been closed for a long time, allowing the voltage across the capacitor to reach a steady-state condition. When the switch is opened, the voltage on the capacitor will generate a current in opposite direction of ic shown in the circuit below, and the capacitor will start to discharge exponentially.
Fig. 2.1
Procedure:
Construct the circuit of Fig. 2.1 on your breadboard.
R = 200 k ; Use two 100k resistors
Measure the actual value of R1 and R2.
R1(measures) = ______
R2(measures) = ______
RT = R1(measures) + R2(measures) = ______
Close the switch and monitor the voltage across the capacitor by connecting a voltmeter across the capacitor. When the voltage reached the steady-state condition.
One time constant ( = RT.C) occurs when the voltage across the capacitor drops to 37% of its final value. If the switch is opened at t = 0 sec, the time constant occurs when the voltage across the capacitor reaches 3.33 volts.
Note: Electrolytic capacitors are polarized, i.e. they have a + terminal and a - terminal. Be sure to connect the + terminal to the positive supply and the - terminal to ground. If connected backwards, an electrolytic capacitor stops being a capacitor and conducts a large DC current. This current can heat up the capacitor to the point where it may EXPLODE. Unfortunately it's not immediately obvious by looking at most electrolytic capacitors, which terminal is positive and which is negative. Most are marked only on the negative terminal, and not with a simple minus sign, but a "minus inside an oval" symbol ( ).
Open the switch and use a stopwatch or the "Clock" program from the "Accessories" menu, to record the time when the voltage across the capacitor reaches 3.33 volts.
(measured) = ______
Use the measured values of and RT to calculate the value of the capacitance of the capacitor.
C = ______
Use Agilent VEE to set up the block program shown in Fig. 2.2. The concept of VEE programming resembles that of program flow chart. A box represents each instruction or I/O operation. Boxes are in turns connected with data flow paths (wires).
The voltage across the capacitor is red from the voltmeter every second for 120 seconds and it is plotted using XY plot display from Agilent VEE. At the same time, the theoretical values are plotted using Agilent VEE formula object. Type the following formula in the formula object.
Where
Vdc =10 V
R = RT(measured)
C = C (calculated)
Fig. 2.21
The voltage across the capacitor will drop exponentially to reach zero voltage. Using Agilent VEE program, obtain the natural response of the RC circuit ( Vc vs. time ) mathematically (using the measured values of R & C) and experimentally. Monitor the voltage at least for 5 (time constant).
Compare the two plots (the experimental and the theoretical plot) obtained from Agilent VEE. Comment on the accuracy of the results. What contributed to the inaccuracy between the two plots.
Computer Simulation:
Using Pspice, simulate the step response of the RC circuit (Fig. 2.3).
Fig. 2.3
The switch part in Pspice has internal resistance when the switch is closed and opened. If the resistance of the switch is not small enough when the switch is closed and it is not big enough when the switch is closed, you can adjust the switch internal resistance values by double clicking on the part (Fig. 2.4). Change Ropen to the larger number (For example 10000Meg).
Fig2.4
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