Resonating angular frequency ω = $\frac{1}{\sqrt{LC}}$ = $\frac{1}{\sqrt{5 \times 80 \times 10^{-6}}}$ = 50 rad $s^{-1}$ ∴ Resonance of L and C in parallel can be calculated $\frac{1}{X}$ = $\frac{1}{X_L} - \frac{1}{X_C}$ = $\frac{1}{\omega L} - \omega C$ Impedence of R and X in parallel is given by $\frac{1}{Z}$ = $\sqrt{\frac{1}{R^2} + \frac{1}{X^2}}$ At resonating frequency of series LCR, $X_L$ = $X_C$ So, $\frac{1}{X}$ = $\frac{1}{X_L} - \frac{1}{X_C}$ = 0 Thus, impedances Z = R and will be maximum. Hence, in parallel resonant circuit, current is minimum at resonant frequency. Current through circuit elements $I_R$ = $\frac{E_V}{R}$ = $\frac{230}{4}$ = 5.75 A $I_C$ = $\frac{E_v}{X_L}$ = $\frac{230}{\omega L}$ = $\frac{230}{50 \times 5}$ = 0.92 A $I_C$ = $\frac{E_v}{X_L}$ = $\frac{230}{\frac{1}{\omega C}}$ = 230 × 50 × 80 × $10^{-6}$ = 0.92 A Since, IL and IC are opposite in phase, so net current, $I_v$ = $I_R + I_L + I_C$ $I_v$ = 5.75 + 0.92 $\sqrt{2}$ sin(ωt – π/2) + 0.92 $\sqrt{2}$ sin(ωt + π/2) $I_v$ = 5.75 – 0.92 $\sqrt{2}$ cos ωt + 0.92 $\sqrt{2}$ cosωt $I_v$ = 5.75 A