CBSE Class 12 · 2005 · All India · Alternating CurrentShort Answer

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Mention the factors on which the resonant frequency of a series LCR circuit depends. Plot a graph showing the variation of impedance of a series LCR circuit with the frequency of the applied a.c. source.

Solution

The resonant frequency is

f_{r} = \frac{1}{2 π L C}

so it depends only on the inductance

L

and the capacitance

C

, and not on the resistance

R

. The impedance

Z = R^{2} + (ω L - \frac{1}{ω C})^{2}

is large at low and high frequencies and dips to its minimum value

Z = R

f = f_{r}

, giving a V-shaped curve with its minimum at resonance.

CBSE Class 12 Board · 2005 · All India · Subjective

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