RC Circuits. The purpose of this lab is to understand how capacitors charge and discharge.

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1 Department of Physics and Geology Purpose Circuits Physics 2402 The purpose of this lab is to understand how capacitors charge and discharge. Materials Decade Resistance Box (CENCO), 0.1 µf, 0.5µF, and 1.0 µf Capacitors, 2001 Function Generator, GW INSTEK Oscilloscope (GOS-620), red and black cords, clips, and coaxial heads. Theory If a resistor is connected to an AC voltage source that outputs a square-wave signal, then you can observe a square-wave voltage through an oscilloscope connected in parallel to the resistor (Figure 1). However, if one includes a capacitor in the circuit and observe the voltage drop on the capacitor, he can see the square-wave signal modified as shown in Figure 2. The shape of the modified signal depends on the capacitance because a capacitor takes time to charge and discharge, which is quite different from a resistor. Charge gradually Discharge gradually Figure 1. Square wave signal on resistor. Figure 2. Modified wave signal on capacitor. One can analyze the time needed to charge a capacitor to any fraction of the full voltage (V 0 ), and the time needed to discharge the capacitor to any fraction of its full voltage (V 0 ). Illustrated in Figure 3 are some representative fractions, 0.25, 0.50, and Figure 3. Voltage versus time on capacitor.

2 During the charge process, the voltage increases with time as V(t) = V 0 (1 e -t/ ) (1) And during the discharge process, the voltage decreases with time as V(t) = V 0 e -t/ (2) By measuring the time and the voltage ratio, V(t)/V 0, one can easily calculate the product which has the dimension of time and is known as the time constant of the circuit. For example, in Figure 3, if t 2 = seconds (as measured from the start of the rise), then using Eq. (1), we have V (t) / V o = 0.5 = 1 e /, (3) which derives = Similarly if t 4 = seconds (as measured from the maximum), then using Eq. (2), we have which yields = V (t) / V o = 0.75 = e /, (4) Experimental Procedures 1. Observe a square-wave signal in the oscilloscope: Connect a resistance box (select R=1 KΩ) in series to the function generator to form a closed circuit. Be sure to use a square-wave signal in the Function function Generator generator, press 1 K for the RANGE setting, and the coaxial head should connect to the TTL terminal. Connect the oscilloscope to the resistor in parallel to observe a square-wave signal on the oscilloscope (Refer to Image 1). One can pull out both handles of the oscilloscope and rotate them in order to set the device at your preferred height. In addition, one can choose either CH1 or CH2 in the oscilloscope to observe signals as long as you stick with the same one throughout the lab. 0.1 µf capacitor Adjust frequency in the function generator to observe the changes on the square-wave signal in the 0.1 µf Capacitor oscilloscope. In terms of the frequency reading of the function generator, for example, if you press the 1K button, the actual frequency output is 1K multiplied by the fraction shown on the frequency Resistance Box Oscilloscope dial. Set frequency dial to 1.0 for this lab. 0.1 µf capacitor Image 1 Image 2 2

3 2. Insert the 0.1 µf capacitor in the circuit: Connect the oscilloscope in parallel to the capacitor as shown in the diagram below and Image 2. Observe the changes on the square-wave signal on the oscilloscope (Refer to Image 2 and the panel settings in Image 3). Image 3 Image 4 Resistance is still set at 1 KΩ. If the signal on the oscilloscope keeps moving to the left or the right, use the LEVEL knob to stabilize it. The POSITION knobs can move the curve up or down, left or right. 3. Read the number of which correspond to Voltage and time: VOLTS/DIV button refers to the voltages each division (consisting of five small gradations) on the vertical axis represents. TIME/DIV button indicates the time each division on the horizontal axis represents. For example, in Image 4 the full voltage is embodied by about 7 vertical, and the time period is embodied by about 4.8 horizontal. In Image 3, each division on the vertical and horizontal axes represents.5 volts and.2 ms, respectively. Enter the values in Tables 1(a) and 1(b). (Refer to Figure 3 and Eqs. (3) and (4) for t 1 through t 6. ) R= 1000 Ω C=0.1µF Theoretical value = Table 1 (a). Charging circuit t 1 = 0.5 t 2 = 0.75 t 3 = Avg. = 3

4 Percentage error = Table 1(b). Discharging circuit t 4 = 0.5 t 5 = 0.25 t 6 = Percentage error= 4. Repeat Steps 2 and 3, this time using the 0.5 µf capacitor instead of the 0.1 µf capacitor (Refer to Image 5 below): Use the same oscilloscope settings as in Image 3 and enter values in Tables 2(a) and 2(b). R= 1000 Ω 0.5 µf capacitor µf capacitor 0.5 µf capacitor C = 0.5 µf Theoretical value = Image 5 Table 2 (a). Charging circuit t 1 = 0.5 t 2 = 0.75 t 3 = 4

5 Table 2 (b). Discharging circuit t 4 = 0.5 t 5 = 0.25 t 6 = 5. Repeat Steps 2 and 3, this time using the 1 µf capacitor instead of the 0.1 µf capacitor (Refer to Image 6 below): Use the same TIME/DIV setting as in Image 3 but change VOLTS/DIV setting to.1 V and enter values in Tables 3 (a) and 3(b). R= 1000 Ω C=1 µf Theoretical value = 1 µf capacitor Image 6 Table 3 (a). Charging circuit t 1 = 0.5 t 2 = 0.75 t 3 = 5

6 Table 3 (b). Discharging circuit t 4 = 0.5 t 5 = 0.25 t 6 = Making Connections How does the capacitance affect the time to charge and discharge a capacitor? 6