If a resistance of $100\, \Omega$,an inductance of $0.5\, H$,and a capacitance of $10 \times 10^{-6}\, F$ are connected in series to a $50\, Hz$ $AC$ supply,then the impedance is:

The power factor of the given $LCR$ circuit is $1/\sqrt{2}$. Find the capacitance $C$ of the circuit in $\mu F$.

In the given circuit,the $AC$ source has $\omega = 100 \ rad/s$. Considering the inductor and capacitor to be ideal,the correct choice$(s)$ is(are):
$(A)$ The current through the circuit,$I$ is $0.3 \ A$
$(B)$ The current through the circuit,$I$ is $0.3 \sqrt{2} \ A$
$(C)$ The voltage across $100 \ \Omega$ resistor $= 10 \sqrt{2} \ V$
$(D)$ The voltage across $50 \ \Omega$ resistor $= 10 \sqrt{2} \ V$

In a series $LR$ circuit,power of $400 \ W$ is dissipated from a source of $250 \ V, 50 \ Hz$. The power factor of the circuit is $0.8$. In order to bring the power factor to unity,a capacitor of value $C$ is added in series to the $L$ and $R$. Taking the value of $C$ as $(\frac{n}{3 \pi}) \mu F$,then the value of $n$ is $......$

In an $LCR$ series circuit $R=10 \,\Omega, X_L=8 \,\Omega$ and $X_C=6 \,\Omega$. The total impedance of the circuit is ........ $\Omega$.

What will be the impedance of the circuit shown below in $\Omega$?