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Resonance

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Running head: RLC CIRCUITS AND RESONANCE 1

RLC Circuit and Resonance

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RLC CIRCUITS AND RESONANCE 2

Introduction

In most important applications, the RLC circuits make use of its frequency response

characteristics. Consider the circuit in figure 19.1, noting that it is identical to that of fig 18.2

except for the addition of a sinusoidal voltage source whose potential is always given by:

In this case, the angular velocity ω may be set to any value. In analyzing the above circuit, the

only change in Equation 18.10 is that the right side is no longer zero but rather V

o

cos ωt. Thus,

we will have,

The variation with time of the capacitor charge Q will be described by the function which is the

solution for equation 19.3. An assumption will be made that, the solution is sinusoidal with the

same frequency as that of the driving voltage but with a phase voltage.

Note that, figure 19.2 show graphs of (a) Q

o

Vs. ω and (b) theta. Vs. ω with the resonance

frequency ω

o

indicated in each case. Resonance will occur when theta =-90°.

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Running head: RLC CIRCUITS AND RESONANCE RLC Circuit and Resonance Name of Student Name of Professor Course Title Date 1 RLC CIRCUITS AND RESONANCE 2 Introduction In most important applications, the RLC circuits make use of its frequency response characteristics. Consider the circuit in figure 19.1, noting that it is identical to that of fig 18.2 except for the addition of a sinusoidal voltage source whose potential is always given by: In this case, the angular velocity ω may be set to any value. In analyzing the above circuit, the only change in Equation 18.10 is that the right side is no longer zero but rather Vocos ωt. Thus, we will have, The variation with time of the capacitor charge Q will be described by the function which is the solution for equation 19.3. An assumption will be made that, the solution is sinusoidal with the same frequency as that of the driving voltage but with a phase voltage. Note that, figure 19.2 show graphs of (a) Qo Vs. ω and (b) theta. Vs. ω with the resonance frequency ωo indicated in each case. Resonance will occur when theta =-90°. RLC CIRCUITS AND RESONANCE 3 Objectives 1. To further investigate the behavior of RLC Circuits. 2. To become more familiar with the experiment aspects of resonance. Apparatus 1. Oscilloscope 2. Signal generator 3. Circuit board 4. Assorted wires Procedure RLC CIRCUITS AND RESONANCE 4 1. The experiment was set as shown in the figure 19.3. Oscilloscope was connected so that CH1 measured the in ...
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