If $E = 200\,V$,$R = 25\,\Omega$,$L = 2\,H$,and $C = 2\,\mu F$ and the frequency is variable,then the current at $f = 0$ and $f = \infty$ will be respectively:

$A$ charged capacitor discharges through a resistance $R$ with time constant $\tau$. The two are now placed in series across an $AC$ source of angular frequency $\omega = \frac{1}{\tau}$. The impedance of the circuit will be-

$A$ series $R-C$ combination is connected to an $AC$ voltage of angular frequency $\omega = 500 \ rad/s$. If the impedance of the $R-C$ circuit is $R\sqrt{1.25}$,the time constant (in $ms$) of the circuit is:

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

When a coil is connected to a $d.c.$ source of $e.m.f.$ $12 \ V$,the current of $4 \ A$ flows in it. If the same coil is connected to a $12 \ V, 50 \ Hz$ $a.c.$ source,the current flowing in it is $2.4 \ A$. The self-inductance of the coil will be:

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: