$A$ series $LCR$ circuit containing an $a.c.$ source of $100 \text{ V}$ has an inductor and a capacitor of reactance $24 \text{ } \Omega$ and $16 \text{ } \Omega$ respectively. If a resistance of $6 \text{ } \Omega$ is connected in series, then the potential difference across the series combination of inductor and capacitor only is: (in $\text{ V}$)

An inductor and a resistor are connected in series to an $AC$ source. The current in the circuit is $500 \,mA$, if the applied $AC$ voltage is $8 \sqrt{2} \,V$ at a frequency of $\frac{175}{\pi} \,Hz$, and the current in the circuit is $400 \,mA$, if the same $AC$ voltage at a frequency of $\frac{225}{\pi} \,Hz$ is applied. The values of the inductance and the resistance are respectively:

$A$ radio can tune over the frequency range of a portion of $MW$ broadcast band: ($800 \;kHz$ to $1200 \;kHz$). If its $LC$ circuit has an effective inductance of $200 \;\mu H$,what must be the range of its variable capacitor?

$A$ charged capacitor discharges through a resistance $R$ with time constant $\tau$. The two are now placed in series across an $AC$ source of angular frequency $\omega = \frac{1}{\tau}$. The impedance of the circuit will be

In a series $LCR$ circuit,the voltage across the resistance,capacitance,and inductance is $10 \, V$ each. If the inductor is short-circuited,what will be the voltage across the capacitor?

$A$ coil of resistance $450 \Omega$ and self-inductance $1.5 \text{ H}$ is connected to an $A$.$C$. source of frequency $\frac{150}{\pi} \text{ Hz}$. The phase difference between voltage and current is