Question

In 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. Find
(1) frequency at which resonance occurs
(ü) current in the circuit at resonant condition.​

Answer 1

$\sf{\huge{\underline{\orange{Given :-}}}}$

• 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