1.

In a series LCR circuit in which R=3 ohm ,L=25 mH and 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»

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  • 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


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