### RLC Series Circuit Pre-lab Assignment

1. In a series RLC circuit it can be helpful to find the circuit's equivalent resistance, known as the impedance. This can be done using the impedance triangle (see Simulation 1). First you determine XL and XC, the inductive reactance and capacitive reactance, respectively. These represent the effective resistance of the inductor and capacitor, respectively. The impedance is the vector sum of XL, XC and R.

(a) If you know the frequency f, the inductance L, and the capacitance C, how do you find XL and XC?

(b) If the resistance in the simulation is set to 5 ohms, what is the maximum current that can be produced? Find a combination of L, C, and frequency that produces this maximum current. Comment on whether there is only one such combination, or whether you could find more than one.

2. Use the second simulation to find the resonant frequency and the two half-power points (the frequencies where the power dissipated in the circuit is 1/2 the power dissipated at resonance). Compare what you measure for the difference between the half-power points, in rad/s, to the theoretical value of Δω = R/L. The two circuits are identical aside from their capacitance. There are two graphs available, one showing voltage across each component as a function of time and the other showing rms current as a function of frequency. Un-check the "Voltage" box to see the current graph, which is more useful here, and note that the frequency units are Hz.

Define f1 as the frequency of the half-power point below the resonant frequency fo, and f2 as the frequency of the half-power point above the resonant frequency.

Circuit fo (Hz) f1 (Hz) f2 (Hz) Δf = f2 - f1 (Hz) Δω= 2πΔf (rad/s) R/L (s-1)
Circuit 1
Circuit 2