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. Current lags the voltage
• B. Resistance in the circuit is 250 $\sqrt{3}\Omega$
• C. Reactance in the circuit is 250 $\Omega$
• D. Average power dissipation in the circuit is 20 $\sqrt{3}$ W

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Current lags the voltage
B Average power dissipation in the circuit is 20 $\sqrt{3}$ W
C Resistance in the circuit is 250 $\sqrt{3}\Omega$
D Reactance in the circuit is 250 $\Omega$

For option (A) Solution :

Expression of voltage of time t: $v=v_m$ ($\sin \omega t+\varphi$)

Expression of current of time t: $i=i_m$ ($\sin \omega t$)

At t = 0 ; $100=200\sin \varphi \Rightarrow \varphi =\frac{\pi }{6}$ rad ; current lags voltage by $\frac{\pi }{6}$ rad
For option (B) Solution : $R=Z\cos \varphi =\frac{V}{I}\cos \varphi =\frac{200V}{400mA}cos\frac{\pi }{6}=250\sqrt{3}\Omega$
For option (C) Solution : $X=Z\sin \varphi =\frac{V}{I}\sin \varphi =\frac{200}{400}\sin \left(\pi /6\right)=$$250\Omega$
For option (D) Solution : $P_{av}=\frac{V_m{I}_m}{2}cos\varphi =20\sqrt{3}W$