BEGINNER'S BOX - 3

For the circuit shown in figure, write down the instantaneous current through each element. 

A variable frequency $230 \mathrm{V}$ alternating voltage source is connected across a series combination of $L=5.0 \mathrm{H}, C=80 \mu \mathrm{F}$ and $R=40 \mathrm{\Omega }$. Calculate amplitude of current at the resonance frequency. 

 A coil of resistance $R$ and inductance $L$ is connected in series with a capacitor $C$ and a complete combination is connected to a.c. voltage. Circuit resonates when the angular frequency of the supply is $\omega ={\omega }_0.$ Find out the relation between ${\omega }_0$, $L$ and $C$. 

Find the phase difference between voltage and current in a series LCR circuit at half-power frequencies.