In this experiment, we explored how capacitors change a circuits response to a sudden change in voltage. Capacitors store energy in an electric field, which prevents sudden voltage drop throughout the circuit. We set up a simple RC circuit and test manual switching, as well as sending a square wave signal through it and measured the voltage drop across the capacitor.
Diagram of the circuit modeled
Before setting up the circuit, we ran some calculations to determine the theoretical time constant, Tao. We used R_1 = 1 kOhm, R_2 = 2.2 kOhm, and C = 20 uF.
Actual resistor values used
Actual breadboard circuit
Charge voltage across the capacitor using trigger
Discharge voltage across the capacitor using trigger
Voltage over time across the capacitor when implementing a square wave
The discharge time of a capacitor is typically ~ 5 time constants, which we calculated to be 15 ms. In other words, the theoretical charge/discharge time should have been approximately 75 ms. The graph shows that the total charge/discharge time of the capacitor in the circuit was nearly spot on.
Lab 18: Passive RL Natural Circuit Response
In this experiment, we explored how inductors change a circuits response to a sudden change in current. We ran essentially the exact same lab as the one above, but we swapped the capacitor for an inductor and used Ohm's law to calculate the change in current across the circuit when the voltage supply is switched on and off.
Diagram of the circuit
Calculations to determine the time constant,Tao
Actual breadboard circuit
Inductor discharge using manual trigger
Voltage across inductor using a square wave
In the calculations above, the time constant was found to be 1.45 microseconds, and thus, the time for discharge should be ~ 6 - 7 microseconds. The manual trigger showed this result exactly, but the square wave did not, likely because the frequency was slightly too high.
In Class Examples
1. Given the circuit below, find Vc(T) and Ic(t) given that Vc(0) = 10V.
2. The switch in the circuit shown below has been closed for a long time. At t = 0, the switch is opened. Calculate i(t) for t > 0.
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