Lecture-17-03-18-08

Lecture-17-03-18-08 - Lecture-17 Resonance in LRC Circuit...

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1 Lecture-17 Resonance in LRC Circuit Forced Harmonic Oscillation If LRC circuit is driven by AC source with V Drive , then The current in circuit maximizes when drive frequency ω Drive equals circuit’s own LRC . Total circuit resistance against the current is at minimum. The total circuit resistance, i.e., impedance , can be calculated by “phasors.” Note that under steady state condition, rms values can be used for I, V R , V L , V C : V R rms Square Root of <V R 2 > , where Thus V R rms I rms R V L rms I rms X L , where X L = L V C rms I rms X C , where X C = ( C) -1 t V C Q dt dQ R dt Q d L D o sin 2 2 = + + 2 2 2 0 2 2 0 2 2 1 ) ( sin 1 ) ( 1 2 R I dt t R I T dt IR T V o T o T R = = >= <
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2 t = 0 t > 0 Kirchhoff’s Loop Rule in Phasor Diagram In detail, at t >0 Here, total impedance Z is given by ( ) () Z I X X R I V V V V V C L C L R 0 2 2 0 0 2 0 0 2 0 2 0 + = + = 2 2 0 0 1 + = = C L R I V Z ω
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3 Sample Calculation of Circuit Impedance Given that R = 10.0 Ω , L = 0.10 H, and C = 0.30 μ F,
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Lecture-17-03-18-08 - Lecture-17 Resonance in LRC Circuit...

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