EEGR 203 – Intro to Electrical Lab Mobile Studio (MS) Lab 8 – RC Circuits and Time Constant Definition: “The time constant of a circuit is defined as the time required for the response to decay by a factor of 1/e (1/e= 0.3678) of its initial value”. This implies that the time constant is the time required for the response to decay to 37% of the initial value”. We can make the assumption that after 5 time constants (e-5= 0.00674) the stored voltage in the capacitor is fully discharged because its final value is less than 1% of this initial value  this is known as the “5 tau rule”. Figure 1: Simple RC Circuit • • Step#1: Build the circuit shown in Figure#1, with the resistor R replaced by a variable resistor (10Kohm Potentiometer) and C = 1 uF . Assume the source is a square wave with a peak voltage of Vpp = 1.5 Vpp and a frequency = 250 Hz. Connect your input AWG1 to Node A and measure the output A2SE by connecting it to Node B. Step#2: start varying the value of R using the potentiometer such that your picture looks like the one shown in Figure#2. Next, capture and save the output observed at node B, with channel#1 showing Vin (square wave) and channel#2 showing Vout (across the capacitor). Make sure you select the AWG1 input for channel 1 and the A2SE input for channel 2. Your screen capture should look similar to that shown in Figure#2, but don’t expect to get the same answer since we are using different resistors and capacitors. Analysis of Results: We will complete the following steps to predict the value of R • Step#3: Look at your screen capture for the capacitor voltage Vout: how long does it take for the capacitor to fully discharge ? You can do this by measuring the time on the X-axis. • Step#4: Use the time you measured to compute the time constant of your circuit. Don’t forget to use the “5 tau rule”. Created by: Dr. Yacob Astatke -1- Fall 2010 • • • • • • Step#5: Use the calculated value of the time constant to predict the value of the variable resistor R. Step#6: Carefully remove your variable resistor from your circuit (without touching the wiper handle) and measure the actual value of the resistor using a DMM. Step#7: Compare the predicted value and the measured value of R. How close are the two values? Step#8: Replace the C = 1 uF capacitor in Figure#1, by a new C = 0.47 uF capacitor and repeat all the steps listed in step#3- steps#7. Step#9: Replace the C = 1 uF capacitor in Figure#1, by a new C = 2.2 uF capacitor and repeat all the steps listed in step#3- steps#7. Write a discussion based on your observations of the results in steps#3 to steps#8. Figure 2: Response of RC Circuit to a square wave Extra-Credit • Keep the circuit in Figure #1 and replace the frequency of the source from 250Hz to 500 Hz. What do you expect the output voltage Vout to look like for C=1uF, C=0.47uF, and C=2.2uF ? How does it affect the RC time constant of the circuit for C=1uF, C=0.47uF, and C=2.2uF ? Explain and justify your answer theoretically and by including screen captures of your MS software. Created by: Dr. Yacob Astatke -2- Fall 2010
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