One application of LRC series circuit is to high pass or low pass filters, which filter out either the low or high frequency components of a signal. A high pass filter is shown in figure, where the output voltage is taken across the LR combination, where LR combination represents an inductance coil that also has resistance due to large length of the wire in the coil.
(i) Find the ratio V out /V s as a function of the angular frequency ω of the source:
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Ans.
(i)
Sol. The voltage across the resistor and the inductor are 90º out of phase. Hence,
V out = 
X L = ω L, X C = 
Hence, Z = 
I = 
and V out = I 
= V s 
∴ 
= 
(ii)
Sol. As ω gets small,
R 2 + 
→ 
∴ 
= 
= R ω C
(iii)
Sol. As ω gets large.
R 2 + 
= R 2 + ω 2 L 2 = ω 2 L 2 
= 
= 1
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