$A$ sinusoidal voltage $V_0 \sin \omega t$ is applied across a series combination of resistance $R$ and inductance $L$. The amplitude of the current in this circuit is

An $AC$ voltage $V = 5 \cos(1000t) \text{ V}$ is applied to an $L-R$ circuit of inductance $3 \text{ mH}$ and resistance $4 \text{ } \Omega$. The value of maximum current in the circuit is . . . . . . $A$.

The power factor of an $RL$ circuit is $1/2$. If $R = 100 \, \Omega$,what is the value of $L$? The frequency of the $AC$ source is $50 \, Hz$.

$A$ light bulb and an open coil inductor are connected to an $AC$ source through a key as shown in the figure. The switch is closed and after some time,an iron rod is inserted into the interior of the inductor. Does the glow of the light bulb $(a)$ increase,$(b)$ decrease,or $(c)$ remain unchanged? Give your answer with reasons.

For the $AC$ circuit shown below,the phase difference between emf and current is $\frac{\pi}{4}$ radian as shown in the graph. If the impedance of the circuit is $1414 \Omega$,then the values of $P$ and $Q$ are

An inductor and a resistor are connected in series to an $AC$ source. The current in the circuit is $500 \,mA$, if the applied $AC$ voltage is $8 \sqrt{2} \,V$ at a frequency of $\frac{175}{\pi} \,Hz$, and the current in the circuit is $400 \,mA$, if the same $AC$ voltage at a frequency of $\frac{225}{\pi} \,Hz$ is applied. The values of the inductance and the resistance are respectively: