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Alternating Current — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsAlternating Current3 Marks
Question
A series $\text{LCR}$ circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit. Plot a graph to show the variation of current with frequency of the source, explaining the nature of its variation.
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Answer



Resultant potential across $\text{LCR}$
$\text{V}^{2} = \text{V}^{2}_{\text{R}} + (\text{V}_{L} - \text{V}_{c} ) ^{2}$
$\text{V}_{R} = \text{iR},\text{V}_{L} = \text{i}\text{X}_{L},\text{V}_\text{c} = \text{i X}_{c}$
On solving
$\text{Z} = \sqrt{\text{R}^{2} + (\text{X}_{L} - \text{X}_{C})^{2}}$
With increase in $ω$, current first increases $($up to $ω_o )$ and then decreases.

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