A choke coil and capacitor are connected in series and the current through the combination is maximum for AC of frequency n. If they are connected in parallel, at what frequency is the current through the combination minimum?

When the X_L is in resonance with X_C, then the current is minimum and the frequency is given as 

$\mathrm{f}=\frac{\omega }{2\pi }$

We have been given series frequency as

$\mathrm{f}=\frac{\omega }{2\pi \sqrt{\mathrm{LC}}}=\mathrm{n}$

By substituting the value in above equation we get

$\mathrm{f}=\mathrm{n}\sqrt{\mathrm{LC}}$

The current through a parallel LC circuit is given as

$I=\frac{V}{Z}$

When the impedance is maximum the current through a circuit is minimum. Hence the frequency will be n.