### RLC Series Circuit Pre-lab Assignment

1. In the RLC Series Circuit experiment you will measure the difference between the half-power points, the two frequencies where the power dissipated in the circuit is 1/2 the power dissipated at resonance. The lab manual states that the difference between the half-power points, in rad/s, is:
Dw = R/L. Prove that this is true. Hint: the average power in the circuit is:
P = Irms2 R, so with R constant the power is reduced by a factor of two when the current is reduced by a factor of 21/2. What is Z at the half-power points? What is |XL-XC| at the half-power points? Starting from there, show that Dw = R/L.

2. Use the simulation to find the resonant frequency, the two half-power points, and then compare to the value from R/L. The 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 angular frequency of the half-power point below the resonant frequency fo, and f2 as the angular frequency of the half-power point above the resonant frequency.

Circuit fo (Hz) f1 (Hz) f2 (Hz) Df = f2 - f1 (Hz) Dw = 2pDf (rad/s) R/L (s-1)
Circuit 1
Circuit 2