In a $L-R$ circuit of $4 \text{ mH}$ inductance and $3 \text{ } \Omega$ resistance, e.m.f. $E = \cos(1000t) \text{ V}$ is applied. The amplitude of current is (in $\text{ A}$)

In a series $CR$ circuit shown in the figure,the applied voltage is $10 \, V$ and the voltage across the capacitor is found to be $8 \, V$. Then the voltage across $R$,and the phase difference between the current and the applied voltage will respectively be:

$A$ light bulb connected in series with a capacitor and an $a.c.$ source is glowing with certain brightness. On reducing the value of capacitance and frequency respectively, the brightness of the bulb

When $80 \ V$ $d.c.$ is applied across a solenoid,a current of $0.8 \ A$ flows in it. When $80 \ V$ $a.c.$ is applied across the same solenoid,the current becomes $0.4 \ A$. If the frequency of $a.c.$ source is $50 \ Hz$,the impedance and inductance of the solenoid are nearly:

In a circuit,$L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45^o$. The value of $C$ is

The time constant of the given $LR$ circuit is $\tau$. If the battery is replaced by an $AC$ source having voltage $V = V_0 \cos \omega t$,the power factor of the circuit will be