$A$ 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 $

When an $AC$ source of emf $E$ with angular frequency $\omega = 100 \text{ rad/s}$ is connected across a circuit, the phase difference between $E$ and current $I$ in the circuit is observed to be $\frac{\pi}{4}$ as shown in the figure. If the circuit consists of only $RC$ or $RL$ in series, then:

An inductor of $\left(\frac{100}{\pi}\right) mH$,a capacitor of capacitance $\left(\frac{10^{-3}}{2 \pi}\right) F$,and a resistor of $10 \Omega$ are connected in series with an $AC$ voltage source of $110 \text{ V}, 50 \text{ Hz}$. The tangent of the phase angle $\phi$ between the voltage and the current is:

$A$ capacitor of $\frac{2.5}{\pi} \mu F$ and a resistor of $3000 \, \Omega$ are connected in series with a $200 \, V, 50 \, Hz$ $AC$ source. What are the power factor and the power dissipated,respectively?

$A$ resistor of $20 \ \Omega$ and a capacitor are connected in series with an $AC$ current source of $50 \ Hz$. What should be the capacitance to produce a phase difference of $30^\circ$ between the voltage and current?

$A$ 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 $...... \Omega$.