Experiment 7: RC Circuits, Exercises of Basic Electronics

Download Experiment 7: RC Circuits and more Exercises Basic Electronics in PDF only on Docsity! Experiment 7: RC Circuits Introduction Capacitors are used in timing circuits in many devices. The time that your dome lights inside your car stay on after you turn off your cars ignition at night is one example of how a capacitor can be used to maintain the lighting long enough for you to remove the keys and collect your things before exiting. The value we use to characterize these kinds of circuits is given by the time constant defined as: τ = RC, where R is the circuit resistance (your dome light in this case) and C is the capacitance, in Farads (F). In this lab, we will measure the time constant of different capacitors in two situations - one where the time constant is several seconds long, and the other for time constants on the order of several milliseconds long. Consider the following RC circuit (figure 1). It contains a source of power (either DC or AC), a resistor R, and of course a capacitor C. If at time t = 0 the Switch A is closed (Switch B remains open), charges will begin to build up in the capacitor. These charges do not accumulate within the capacitor instantaneously due to the “resistance” provided by the resistors. The potential difference across the capacitor can be expressed as V (t) = Vo ( 1 − e−t/τ ) (1) where τ = RC , and V0 is the maximum potential difference across the capacitor. After a sufficiently long time (much larger than the time constant), if Switch A is opened while Switch B is closed, the capacitor will discharge all of its accumulated charges. The potential difference across the capacitor for this process can be expressed as V (t) = Voe −t/τ (2) C R V(t) + - A B Figure 1: Circuit for RC charge-discharge measurement where V(t) is the sensor used to measure the potential difference across the capacitor as a function of time. The time dependence of the potential difference V(t) for the charging and discharging process is shown in Figure 2. The time constant can be determined by observing either the charging or discharging process. For the charging process, τ is equal to the time for V(t) to reach 63% of its “final” value. For the discharging process, τ is equal to the time for V(t) to fall 63% from its initial value. These values can actually be measured at any time during the charging or discharging cycle, as long as one waits long enough for the capacitor voltage to increase or decrease by 63% of a measured value. If one can capture the voltage passing 9V during a discharge cycle, then one only needs to measure the time it takes for the voltage to decrease by 5.7V to 3.3V(a 63% decrease). You will practice this latter approach with the next exercise. 1 Time 37 63 100 V (t )/ V o ττ 5 divisions 3 divisions 8 divisions Figure 2: Potential difference across a capacitor in an RC circuit as a function of time. Part 1 - Measurement of a Long Time Constant: In this experiment, you will measure V(t) across the capacitor as it discharges. First measure the capacitance of the large capacitor provided using a capacitance meter (the nominal value is 47 µF) . Then put on safety glasses, and construct the circuit as shown in Figure 3, making sure the electrolytic capacitor is connected with correct polarity. The act of connecting or disconnecting the wire between the battery and breadbord functions as the switch. To monitor the voltage use a voltage sensor connected to the 850 Universal Interface. Notice that when the capacitor is connected to the battery, current will flow until the capacitor is completely charged. When the battery is disconnected, the capacitor discharges through the voltage sensor, and interface. The interface contains an internal resistor Ri, which acts as the “load” resistor for the circuit. In other words, the resistor in the 850 Universal Interface is the R in the RC circuit. The internal resistor is given as Ri = 1 MΩ. Use the Capstone software to set up a dispaly containing a two column table, and select voltage in the first column, and time in the second column. Then find the controls tab near the bottom of the window, and adjust the sample rate for the voltage sensor to 1 Hz (1 measurement per second). + - C R VS i V Micronta Multimeter PASCO Capstone Sensor Figure 3: Setup for RC circuit with large capacitor and a resistor (Ri) from inside the voltage sensor. 2