Question

In the circuit shown, resistance $R=100\Omega$ , inductance $L=\frac{2}{\pi }H$ and capacitance $C=\frac{8}{\pi }\mu F$ are connected in series with an ac source of 200volt and frequency 'f '. If the readings of the hot wire voltmeters $V_1$ and $V_2$ are same then

• A. f = 125 Hz
• B. $f=250\pi Hz$
  
• C. current through R is 2A
  
• D. $V_1=V_2=1000$ volt

Answer 1

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

The correct options are
A f = 125 Hz
C current through R is 2A

D $V_1=V_2=1000$ volt

$V_1=V_2\Rightarrow X_L=X_C\Rightarrow f=\frac{1}{2\pi \sqrt{LC}}=25Hz$

$I_0=\frac{V_0}{R}=\frac{200}{100}\because X=0\therefore Z=R$

$I_0=2A$

$V_1=V_2=I=I\omega L=2\times 2\pi \times 125\times \frac{2}{\pi }=1000$volt