Question

If resistance $R=100\Omega$ , inductance $L=\frac{2}{\pi }H$ and capacitance $C=\frac{8}{\pi }μF$ are connected in series with an AC source of $200volt$ and frequency $f$ as shown in the circuit. If the readings of the hot wire voltmeters $V_{1}$ and $V_{2}$ are same then which among the following statements is wrong?

• 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: (B)

$V_{1}=V_{2} \, $ $\Rightarrow x_{L}=x_{c}$
$\Rightarrow f=\frac{1}{2 \pi \sqrt{LC}}=125 \, Hz$
$I_{0}=\frac{V_{0}}{R}=\frac{200}{100}$ $\left(\right.\because x=0 \, \, \therefore \, \, z=R\left.\right)$
$=2A$
$V_{1}=V_{2}=1X=1.\left(\right.ωL\left.\right)=2\times 2\pi \times 125\times \frac{2}{\pi }$
$V_{1}=V_{2}=1000 \, volt$