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

$Z=\sqrt{{R^2}+\left (2\pi\,fL-\frac{1}{2\pi\,fC} \right )^2}$
From above equation at f = 0 $\Rightarrow Z = \infty$
$When\,\,f = \frac{1}{{2\pi \sqrt {LC} }}\,\,(resonantfrequency)\,\, \Rightarrow Z = R$
$For\,\,f > \frac{1}{{2\pi \sqrt {LC} }} \Rightarrow z\,\,starts{\text{ }}increasing$
i.e., for frequency 0 – f_r, Z decreases
and for f_r to $\infty$ , Z increases. This is justified by graph c

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