AP Physics RC Circuit Lab
1. Using the Pasco electronics board, two 2 KW resistors (or two other identical resistors in the 1-10 KW range), a 470 mF capcacitor, and two 1.5 V D-Cell batteries, concstruct the network shown. The button switch on the Pasco board when pressed down will complete the circuit. Measure the potential across the capacitor as a function of time with a Vernier digital voltmeter and the Logger Pro software.
2. When the circuit is built, test the circuit using in Logger Pro. Assure quality data by setting the sampling rate (Menu>Experiment>Data Collection) to 50 samples per second, Length 10 seconds (at least). After starting the collection, press the switch for 3-5 approximately five seconds and then release, contining to acquire data for approximately 5 more seconds. You should see a wave form like the figure below. If not, check your circuit.
3. Now go back to the Data Collection Window and select the triggering tab. Check “Triggering” and “Increasing”.
4. Clear your data and start a new collection. Data acquisition should not actually begin until the switch is pressed and the voltage across the capacitor begins to rise. If it starts prematurely you may have to zero the sensors. Hold the switch down for several seconds until the voltage reaches its asymptotic value.
5. Select the data from t=0 to a time when the asymptote is reached and perform a curve fit using the appropriate formula (see figure at right). Record the values for A, C and B. Print out the plot for your records. Note the number of seconds between t=0 and when the capacitor potential has reached its maximum value.
A: ______
B: ______
C: ______
6. Repeat step #3, except change “Triggering” to “Decreasing”.
7. Begin a new acquisition. Hold down the switch for the time interval required for the capacitor to achieve its maximum potential and then release. Acquisition should begin and you should see the voltage exponentially decay.
8. Select the data from t=0 through a time when the decay curve has reached zero and perform a curve fit using the decaying exponential: A*exp(-Ct)+B. Record the values of A, B, and C.
A: ______
B: ______
C: ______
Discussion:
1. The values for A in #5 and #8 above should be (nearly) the same. Explain, in terms of the values of the components in the circuit, why A have the value that it has.
2. Compare the values of C in #5 and #8. How do these relate to the time constants of the circuit? (if you used identical resistors in the circuit the value for C in #5 should be approximately twice the value for C in #8).
3. For steps 6-8, the capacitor is discharging through capacitor R2, following the theory (this equation is derived in the text). For steps 3-5, the charging equation for the circuit is . If R1=R2=R, then we have . You can see that Q0 = VC/2. Why is this true, rather than, say, Q0 = VC?
4. The charging equation in #3 above is different from the one derived in the text when a single resistor is in the circuit. This can be derived by using Kirchhoff’s rules to obtain a differential equation in terms of Q, V and the resistors.
Junction rule:
Loop rule:
Loop rule again:
Note that , and eliminate i1 and i2 by substitution to obtain .
This equation can be integrated to obtain the charging equation above. Filling in the details of this derivation is one of the problems on the take home exam.
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