In today's lab, we explored the response of a series RLC circuit, which contains one resistor, one capacitor, and one inductor all connected in series, with a power supply feeding a step function into the circuit. We began by modeling the circuit in order to determine our expectation values for running the experiment. The circuit under investigation is pictured below:
In this lab, Vin = 2V (step), R = 1 Ohm, L = 1 uH, and C = 0.47 uF. Before building the circuit, we ran some calculations to determine the characteristic function that the circuit should follow:
Next, we built the circuit according to the schematic provided in the lab manual, using the corresponding circuit elements.
Since we found the nepper frequency to be less than the resonant frequency, the system should operate as an underdamped circuit. Thus, when the step function turns the voltage off, we should see a graph that looks like a sinusoidal wave that gets smaller and smaller in amplitude over time.
As shown in the graph, we measured the voltage across the capacitor, and observed the exact behavior from the circuit that was expected. The initial voltage, V(0) = 2V, and when the voltage supply is switched off, the voltage across the capacitor behaves as a sinusoidal wave that decreases in amplitude over time.
In Class Examples
1. The switch in in the circuit below has been closed for a long time. It is open at t = 0.
Find: (a) i(0+), v(0+), (b) di(0+)/dt, dv(0+)/dt, (c) i( ∞ ), v( ∞ ).
2. In the second example, we mathematically derived the characteristic equation of a series LRC Circuit:
3. In the figure R = 40 ohms, L = 4 H and C = ¼ F. Calculate the characteristic roots of the circuit. Is the natural response overdamped, underdamped or critically damped?
4. In the parallel circuit shown, find v(t) for t > 0, assuming v(0) = 5 V, i(0) = 0, L = 1 H, and C = 10 mF R = 1.923 Ohms.
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