An alternating voltage is applied to a series $LCR$ circuit. If the current leads the voltage by $45^{\circ}$,then $\left(\tan 45^{\circ}=1\right)$:

$A$ resistance of $200 \ \Omega$ and an inductor of $\frac{1}{2 \pi} \ H$ are connected in series to an a.c. voltage of $40 \ V$ and $100 \ Hz$ frequency. The phase angle between the voltage and current is

An inductor of reactance $1 \Omega$ and a resistor of resistance $3 \Omega$ are connected in series to the terminals of a $10 \ V$ (rms) $AC$ source. The power dissipated in the circuit is (in $W$)

An inductance coil has a resistance of $100 \Omega$. When an $A.C.$ signal of frequency $100 \ Hz$ is applied to the coil,the voltage leads the current by $45^{\circ}$. The inductance of the coil in henry is $\left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right]$

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

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