The A.C. circuit shown in figure. Find the frequency ( $ω_{0}$ ) of the AC voltage source so that current through the source will be in same phase as of voltage of source.

Question

The A.C. circuit shown in figure. Find the frequency ( ω 0 ​ ) of the AC voltage source so that current through the source will be in same phase as of voltage of source.

TestHub · Accepted Answer

From Phasor

Component of current I perpendicular to V should be cancelled

$i_{oc} = i_{R L} sin ϕ$

$tan ϕ = \frac{ω L}{R}$

$\frac{V _{0}}{\frac{1}{ω C}} = \frac{V _{0}}{R ^{2} + ( ω L ) ^{2}} = \frac{ω L}{R ^{2} + ( ω L ) ^{2}}$

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