In a series LCR circuit in which R=3 ohm ,L=25 mHand C = 800 uF a sinu

1.	In a series LCR circuit in which R=3 ohm ,L=25 mHand C = 800 uF a sinusoidal a.c voltage of peakvalue 250 V is applied. Find(1) frequency at which resonance occurs(ü) current in the circuit at resonant condition.
Answer» $\sf{\huge{\underline{\orange{Given :-}}}}$ A SERIES LCR circuit in which R=3 OHM ,L=25 mH and C = 800 uF a sinusoidal a.c voltage of peak value 250 V is applied. $\sf{\huge{\underline{To\:Find :-}}}$ Frequency at which resonance occurs. Current in the circuit at resonant condition. $\sf{\huge{\underline{\green{Answer :-}}}}$ A circuit containing LCR, L = indicator, C = Capacitor, R = Resistor It is CONNECTED to AC SUPPLY. R=3 ohm L=25 mH = 25 × ${10}^{ - 3}$ C = 800 uF = 800 × ${10}^{ - 6}$ Peak value 250 V a.) Frequency at which resonance occurs. ➝ Resonant frequency = $\large{f}$ = $\frac{1}{2\pi \sqrt{LC} }$ ➝ $\large{f}$ = $\frac{1}{2\pi \sqrt{LC} }$ ➝ f = 1/2π× 25 × ${10}^{ - 3}$ × 800 × ${10}^{ - 6}$ ➝1/ 20000 × ${10}^{ - 9}$ ➝1/ 2 × ${10}^{ - 9-4}$ ➝ 1/2 × ${10}^{ - 11}$ ➝ $\large{f}$ = $\frac{1}{2 \times 2 \times {10}^{ - 11}}$ ➝ 2.5 × ${10}^{10}$ rad s-¹ b.) Current in the circuit at resonant condition ➝ I = ${V}\times{ R}$ ➝ I = ${250}\times{ 3}$ I = 83.34 A