In a series resonant circuit, the $AC$ voltages across resistance $R$, inductor $L$, and capacitor $C$ are $5 \,V$, $10 \,V$, and $10 \,V$ respectively. The $AC$ voltage applied to the circuit will be . . . . . . . (in $V$)

In the figure shown,three $AC$ voltmeters are connected. The circuit is at resonance.

An $L-C-R$ series circuit with $100 \, \Omega$ resistance is connected to an $ac$ source of $100 \, V$ and angular frequency $300 \, rad/s$. When the capacitance is removed, the current lags behind the voltage by $45^{\circ}$. When the inductance is removed, the current leads the voltage by $45^{\circ}$. The current flowing in the circuit will be ... $A$.

An $LCR$ series circuit with $100 \Omega$ resistance is connected to an $AC$ source of $200 V$ and angular frequency $300 \text{ rad/s}$. When only the capacitor is removed,the current lags behind the voltage by $60^{\circ}$. When only the inductor is removed,the current leads the voltage by $60^{\circ}$. The power dissipated in the $LCR$ circuit will be:

$A$ resistor of $50 \Omega$,an inductor of self-inductance $(\frac{2}{\pi^2}) \text{ H}$,and a capacitor of unknown capacity are connected in series to an $A$.$C$. source of $100 \text{ V}, 50 \text{ Hz}$. When the voltage and current are in phase,the value of the capacitance is: (in $\mu \text{F}$)

For the series $LCR$ circuit shown in the figure,what is the resonance frequency and the amplitude of the current at the resonating frequency?