[PDF] RLC Circuits - Rice University



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RLC Circuits - Rice University

RLC Circuits

It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.

Richard Feynman (1918-1988)

OBJECTIVES

To observe free and driven oscillations of an RLC circuit.

THEORY

The circuit of interest is shown in Fig. 1, including sine-wave sources. We start with the series connection, writing Kirchoff's law for the loop in terms of the charge q C on the capacitor and the current i = dq C /dt in the loop. The sum of the voltages around the loop must be zero, so we obtain v L +v R +v C =v D sin!t() (1) L d 2 q C dt 2 +R dq C dt q C C =v D sin!t() (2) For reasons that will become clear shortly, we rewrite this as d 2 q C dt 2 2 dq C dt 0 2 q C v D L sin("t) (3) with ! = 2L/R and ! 0 2 =1/LC. Two situations will be of interest. We will examine the free oscillations, when v D is exactly zero, meaning that the sine-wave generator has been replaced with a short circuit. We will then connect the sine wave generator and calculate the response as a function of frequency. R C L v D Fig. 1 Idealized series RLC circuit driven by a sine-wave voltage source.

RLC Circuits 2

If the resistance in the circuit is small, the free oscillations are of the form q C =q C0 equotesdbs_dbs2.pdfusesText_2