Question

The given graph shows volume with time in the source voltage and steady state current drawn by a series $BLC$ circuit:-
Which of the following statements is/are correct?
(a) Current lags the voltage.
(b) Resistance in the circuit is $250\sqrt{\Omega }$.
(c) Reactance in the circuit is $250\Omega$.
(d) Average power dissipation in the circuit is $20\sqrt{3\Omega }$

• A. Only a
• B. a & b
• C. a, b & c
• D. All

Answer 1

The correct option is D All

D. All

A

$v=v_m(\sin wt+\varphi )$

$i=i_m\left(\sin wt\right)$

$at,t=0,100=200\sin \varphi \Rightarrow \varphi =\frac{\pi }{6}rad$

current lags voltage by $\frac{\pi }{6}rad$

B.

$R=Z\cos \varphi =\frac{V}{I}\cos \varphi =\frac{200}{400m}\cos \frac{\pi }{6}$

$=250\sqrt{3}\Omega$

C.

$X=Z\sin \varphi =\frac{V}{I}\sin \varphi =\frac{200}{400m}\sin \frac{\pi }{6}$

$=250\Omega$

D.

$P_{av}=\frac{V_m{I}_m}{2}\cos \varphi =20\sqrt{3}W$