Which graph shows the correct variation of r.m.s. current ' $\mathrm{I}$ ' with frequency ' $\mathrm{f}$ '…
Which graph shows the correct variation of r.m.s. current ' $\mathrm{I}$ ' with frequency ' $\mathrm{f}$ ' of a.c. in case of (LCR) series resonance circuit?
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Solution
In series, $\mathrm{Z}=\sqrt{\left(2 \pi \mathrm{fL}-\frac{1}{2 \pi \mathrm{fC}}\right)^2+\mathrm{R}^2}$
Current, $I=\frac{\mathrm{V}}{\sqrt{\left(2 \pi \mathrm{fL}-\frac{1}{2 \pi \mathrm{fC}}\right)^2+\mathrm{R}^2}}$
As frequency increases, current first increases and then decreases. Current is maximum at resonance when $\mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{C}}$
