The given graph shows variation with time in the source voltage and steady state current drawn by a series RLC circuit.Which of the following statements is/are correct?

Engineering

Physics

Superposition of Current in AC Circuit

AC Circuit Analysis

LCR and Resonance in AC Circuit

Question

The given graph shows variation with time in the source voltage and steady state current drawn by a series RLC circuit.
Which of the following statements is/are correct?

A

Average power dissipation in the circuit is $20 \sqrt{3}$ W

B

Current lags the voltage

C

Resistance in the circuit is 250 $\sqrt{3} Ω$

D

Reactance in the circuit is 250Ω

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For option (A) Solution : Expression of voltage of time t : v = v_m (sin, ωt + ϕ)

Expression of current of time t : i = i_m (sinωt)

At t = 0 ; 100 = 200sinϕ ⇒

ϕ = \frac{π}{6}

rad ; current lags voltage by

\frac{π}{6}

rad
For option (B) Solution :

R = Zcosϕ = \frac{V}{I} cosϕ = \frac{200 V}{400 mA} \cos \frac{π}{6} = 250 \sqrt{3} Ω

For option (C) Solution :

X = Zsinϕ = \frac{V}{I} sinϕ = \frac{200}{400} \sin (π / 6)

= 250Ω
For option (D) Solution :

P_{av} = \frac{V_{m} I_{m}}{2} cosϕ = 20 \sqrt{3} W