First slide

Phasors and Phasor Diagrams

Question

Which one of the following curves represents the variation of impedance (Z) with frequency f in series LCR circuit ?

Moderate

A
B
C
D

Solution

$Z = \sqrt{R^{2} + {(2 πfL - \frac{1}{2 πfC})}^{2}}$
From above equation at $f = 0 \Rightarrow Z = \infty$
When $f = \frac{1}{2 π \sqrt{LC}}$ (resonant frequency) $\Rightarrow Z = R$
For $f > \frac{1}{2 π \sqrt{LC}} \Rightarrow Z$ starts increasing.
i.e., for frequency $0 - f_{r},$ Z deceases and for $f_{r} to \infty, Z$ increases. This is justified by graph (3).

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