Work through this section before going to the lab. Consider the electrical \"RC

Question

Work through this section before going to the lab. Consider the electrical "RC circuit" shown in the illustration. The resistance is R = 10 kohm and the capacitance is C = 0.1muF. Assume that the input voltage source va(t) is sinusoidal, with amplitude of 1 volt. That is, vs(t) = sin(wt). Derive the expression for the steady-state voltage across the capacitor. From this, show the expressions for the amplitude, phase angle, and lag time1 in terms of the appropriate parameters (e.g. the system time constant, the input frequency, etc.). For the frequencies given in the table, find numerical values and fill with the calculated values. Also fill in the corresponding frequency values in rad/sec. You will fill in the measured values in the laboratory. Be sure you understand how the lag time is related to the phase angle.

Explanation / Answer

frequency Amplitude lag time phase angle f Hz w rad/sec calculated calculated calculated 50 314 0.95 -17.4 100 628 0.846 -32.12 200 1256 0.6228 -51.47 500 3140 0.303 -72.3

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