Lab 7 - RC Circuits

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Florida International University *

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MISC

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Electrical Engineering

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Apr 3, 2024

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docx

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Name ___________________________ Date___________________ RC CIRCUIT SIMULATION Introduction In this simulation you will study the behavior of the current and voltages of a RC circuit. In the diagram above we display an RC circuit. When we close the switch S 1 leaving the switch S 2 open, the capacitor is charged through the resistor by the constant voltage source. The voltages across the capacitor and resistor change exponentially with time. The voltage across the capacitor and the resistor are given as, V C ( t )= V (1− e − t / τ ) V R ( t )= V e − t / τ , where V is the applied voltage and τ=RC is the time constant. Once the capacitor is charged we can open the switch, S 1 and then close the switch S 2 . The capacitor will now discharge through the resistor, the voltages across the capacitor and resistor in this case are given by, V C ( t )= V e − t / τ V R ( t )=− e − t / τ , where V is the initial voltage across the capacitor. The rate at which the capacitor charges or discharges is characterized by the time constant τ = RC. When charging , RC is the time that it takes for the capacitor voltage to increase from zero voltage to 0.632 times the charging voltage, since at t = τ = RC V C ( t )= V (1− e −1 ) = V (1 - 0.368) = 0.632 V, or 63% of V Similarly, when discharging , RC is the time for the voltage to drop to 0.368 times its initial value, since at t = RC V C = V e -1 = 0.368 V, or 36.8% of V

1 – Setup Open the link (https://phet.colorado.edu/en/simulation/legacy/circuit-construction-kit-ac-virtual-lab) and run the java applet (you could try this link instead: http://phet.colorado.edu/sims/html/circuit- construction-kit-ac/latest/circuit-construction-kit-ac_en.html Opening this software you will see a blank canvas On the right hand side you will see a list of elements you can add to your circuit. Click the schematic button on the right hand side of the screen. To create a circuit simply click and drag a circuit element onto your canvas. Circuit elements like batteries, capacitors and resistors when dragged onto the canvas have a starting value. To change this value right click on the element. Under the tools section on the right hand side is a stopwatch and a voltmeter. Click on both of these. The voltmeter has probes which can be dragged to different locations in the circuit to measure the voltage across circuit elements. In this lab we will use it to measure the voltage across the capacitor. The switches in the circuit simulator have a loose wire which can be dragged to close the circuit. Create in the circuit simulator the RC circuit shown on the first page. It does not need to looks exactly like it, just match the connections as shown in the circuit in the figure above. Choose the following values for the resistor, the capacitor and the battery: R = 100Ω, C = 0.2F , V = 5V. 2 – Charging a Capacitor To begin make sure your capacitor is discharged. That is the potential difference or voltage across the capacitor is zero. You can use the voltmeter to check that it is zero. If it is not zero we can discharge the capacitor by closing switch 2 and opening switch 1. Once the voltage is zero leave switch 1 open and open switch 2. Since this is a simulation it also gives you the option to right click on the capacitor and choose discharge or charge capacitor. If you choose to do this for your setup make sure both switches are open so the capacitor will remain in the charged/discharged state until you are ready.

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