The impedance of a circuit,when a resistance $R$ and an inductor of inductance $L$ are connected in series in an $AC$ circuit of frequency $f$ is

$A$ student connects a long air-cored coil of manganin wire to a $100\,V$ $D.C.$ supply and records a current of $25\,A$. When the same coil is connected across a $100\,V$,$50\,Hz$ $A.C.$ supply,the current reduces to $20\,A$. The reactance of the coil is....$\Omega $

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

An inductor of inductance $L$ and a resistor of resistance $R$ are joined in series and connected to a source of frequency $\omega$. The power dissipated in the circuit is

In a series $LCR$ circuit,the voltages across the inductance and the capacitance are not

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is