An electric bulb has a rated power of $50 \, W$ at $100 \, V$. If it is used on an $AC$ source of $200 \, V, 50 \, Hz$, a choke has to be used in series with it. This choke should have an inductance of (in $ \, H$)

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

$A$ sinusoidal voltage $V(t) = 210 \sin(3000t) \text{ V}$ is applied to a series $LCR$ circuit in which $L = 10 \text{ mH}$,$C = 25 \mu\text{F}$,and $R = 100 \Omega$. The phase difference $(\Phi)$ between the applied voltage and resultant current will be

In an $LR$-circuit,the inductive reactance is equal to the resistance $R$. If the applied voltage is $E = E_0 \cos(\omega t)$,what is the power dissipated in the circuit?

$A$ 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?

An inductor and a resistor are connected in series to an ac source of variable frequency. When the frequency of the applied ac is $50 \ Hz$,the power factor of the circuit is $\frac{\sqrt{3}}{2}$. If the frequency of the ac is increased by $200 \%$,the power factor of the circuit is . . . . . . .