An inductance of $0.2 \ H$ and resistance of $100 \ \Omega$ are connected in series to an $AC$ of $180 \ V$,$50 \ Hz$ supply. The $RMS$ current flowing in the circuit will be . . . . . . (Take $\pi^2$ as $10$). (in $A$)

An ideal inductor of $\left(\frac{1}{\pi}\right) H$ is connected in series with a $300 \Omega$ resistor. If a $20 \ V, 200 \ Hz$ alternating source is connected across the combination,the phase difference between the voltage and current is

An inductor and a resistor in series are connected to an $A.C.$ supply of variable frequency. As the frequency of the source is increased,the phase angle between current and the potential difference across $L$ will

If a dielectric slab is inserted in the capacitor of the given $RC$ circuit,then the brightness of the bulb will:

In an $LCR$ series circuit,an inductor $30 \, {mH}$ and a resistor $1 \, \Omega$ are connected to an $AC$ source of angular frequency $300 \, {rad/s}$. The value of capacitance for which the current leads the voltage by $45^{\circ}$ is $\frac{1}{x} \times 10^{-3} \, {F}$. Then the value of $x$ is ..... .

An induction coil has an impedance of $10\,\Omega$. When an $AC$ signal of frequency $1000\,Hz$ is applied to the coil,the voltage leads the current by $45^o$. The inductance of the coil is