In the given circuit,the potential difference across the resistance is $54 \, V$ and the power consumed by it is $16 \, W$. If the $AC$ frequency is $60 \, Hz$,find the value of $L$ in $H$.

$A$ capacitor and a resistor of resistance $100 \sqrt{3} \Omega$ are connected in series to an $AC$ source of voltage $V = 100 \sin(200t) \text{ V}$,where $t$ is time in seconds. If the phase difference between the voltage and the current in the circuit is $30^{\circ}$,then the capacitance of the capacitor is: (in $\mu \text{F}$)

In an $A.C.$ circuit,a resistance '$R$' is connected in series with an inductance '$L$'. If the phase angle between voltage and current is $45^{\circ}$,the value of inductive reactance will be $(\tan 45^{\circ} = 1)$.

When a $DC$ voltage of $200\, V$ is applied to a coil of self-inductance $\frac{2\sqrt{3}}{\pi}\,H$,a current of $1\, A$ flows through it. When the $DC$ source is replaced by an $AC$ source of $200\, V$,the current in the coil is reduced to $0.5\, A$. The frequency of the $AC$ supply is......$Hz$.

In an $RL$ circuit,the resistance is $\pi \sqrt{3} \,\Omega$. The phase difference between the current and the voltage is $30^\circ$. The $ac$ frequency is $50 \,Hz$. The inductance is . . . . . . $Henry$.

$A$ 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 $