$A$ coil has inductance of $0.4 \text{ H}$ and resistance of $8 \Omega$. It is connected to an $AC$ source with peak emf $4 \text{ V}$ and frequency $\frac{30}{\pi} \text{ Hz}$. The average power dissipated in the circuit is (in $\text{ W}$)

Mark the incorrect statement.

In an electrical circuit,$R, L, C$ and an $a.c.$ voltage source are all connected in series. When $L$ is removed from the circuit,the phase difference between the voltage and the current in the circuit is $\pi /3$. If instead,$C$ is removed from the circuit,the phase difference is again $\pi /3$. The power factor of the circuit is

Given below are two statements :
Statement $I$ : In an $LCR$ series circuit,current is maximum at resonance.
Statement $II$ : Current in a purely resistive circuit can never be less than that in a series $LCR$ circuit when connected to the same voltage source.
In the light of the above statements,choose the correct option from the options given below :

$A$ $\frac{2.5}{\pi} \mu F$ capacitor and $3000 \, \Omega$ resistor are joined in series to an $AC$ source of $200 \, V$ and $50 \, Hz$ frequency. The power factor of the circuit and the power dissipated in it will respectively be:

Find the peak current and resonant frequency of the following circuit (as shown in the figure).