A series LCR circuit is connected to an a.c. source of $220$ V, $50$ Hz. The circuit contains a resistance $R = 80\,\Omega$, an inductor of inductive reactance $70\,\Omega$ and capacitor of capacitive reactance $130\,\Omega$. The power factor of the circuit is $\dfrac{x}{10}$. The value of x is

Determine the frequency for which a $10\,\mu\text{F}$ capacitor has a reactance of $2 \times 10^{-3}\,\Omega$.

A coil has inductive reactance $3$ H. The ratio of its reactance when it is first connected to an a.c. source and then to d.c. source is

An equiconvex lens of focal length F is cut in to two equal parts along the vertical axis. The focal length of each part will be