An inductive coil of resistance 10 ohms and inductance 0.1H is connected in parallel with 150μf capacitor to a variable frequency at which 200V supply find the resonance at which the total current taken from the supply is in phase with supply is in phase with supply voltage also find value of this current. -

Given:

$$R = 10 Ω \hspace{4cm} \text{Series inductive coil} \\ L= 0.1H \hspace{3.8cm} \text{Series inductive coil} \\ \hspace{1.5cm}C = 150µF = 150 \times 10-6 \hspace{1cm} \text{in parallel with inductive coil} \\ \hspace{1.5cm}V = 200 V \hspace{3.5cm} \text{in parallel with inductive coil}$$

Resonant frequency,

$f_r=\dfrac{1}{2 \pi}\sqrt{\dfrac{1}{LC}-\dfrac{R^2}{L^2}}=\dfrac{1}{2 \pi}\sqrt{\dfrac{1}{0.1 \times150\times10^{-6}}}-\dfrac{10^2}{(0.1)^2} \\ f_r=37.9 Hz$

Dynamic impedance,

$Z_c=\dfrac{L}{CR}=\dfrac{0.1}{150 \times10^{-6}\times10} \\ Z_c=66.67 \Omega$

Circuit current at resonance

$I_r=\dfrac{V}{Z_r}=\dfrac{200}{66.67}\\ I_r=3Amp$

For phasor diagram,

$I_L=\dfrac{V}{Z_L}=\dfrac{200}{\sqrt{10^2+2\times\pi37.9\times0.1}} \\ I_L=17.91 Amp \\ I_c=\dfrac{V}{X_c}=\dfrac{200}{\dfrac{1}{2 \pi \times37.9\times150\times10^{-6}}}$

Phase angle of the coil