Physics - EMI/AC Question with Solution | TestHub

The current will be in phase with voltage when phase angle is zero, 

$\therefore \tan \text{ϕ}=\frac{\text{ω}L-\frac{1}{\text{ω}C}}{R}=0$

Where $\text{ω}, L, C, R$ are the angular frequency, inductance, capacitance and resistance respectively.

$\Rightarrow \text{ω}={\text{ω}}_0=\frac{1}{\sqrt{LC}}$

$\Rightarrow {\text{ω}}_{\text{ο}}$is independent of $R$

$\Rightarrow (resonant frequency) {\text{ω}}_0={10}^6\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}$

Current in the circuit is given by,

$i_0=\frac{V_0}{\sqrt{R^2+{\left(\text{ω}L-\frac{1}{\text{ω}C}\right)}^2}}$

When $$\begin{gathered} \text{ω}\to 0, \\ {i}_0\to 0 \end{gathered}$$

For  $\text{ω}\gg {\text{ω}}_0$ circuit behaves as inductor.