In a series $LCR$ circuit, the voltages across $L, C$, and $R$ are $50 \,V, 20 \,V$, and $40 \,V$ respectively. The $A.C.$ voltage applied across the combination of $LCR$ is: (in $\,V$)

An inductor of reactance $100 \text{ } \Omega$, a capacitor of reactance $50 \text{ } \Omega$, and a resistor of resistance $50 \text{ } \Omega$ are connected in series with an $AC$ source of $10 \text{ V}$, $50 \text{ Hz}$. Average power dissipated by the circuit is (in $\text{ W}$)

Obtain the relation for the voltage applied to a series $LCR$ circuit.

$A$ resistor of resistance $30 \Omega$, an inductor of reactance $10 \Omega$, and a capacitor of reactance $10 \Omega$ are connected in series to an $AC$ voltage source $V = 300 \sqrt{2} \sin(\omega t)$. The current in the circuit is . . . . . . (in $\text{ A}$)

The figure shows an $LCR$ series $AC$ circuit. If $L$ is removed from the circuit,the current leads the voltage by $45^o$,while if $C$ is removed,the current lags the voltage by $45^o$. The current passing in the original circuit is......$A$.

In a series $LCR$ circuit,$R$ represents the resistance of an electric bulb. If the frequency of the $A.C.$ supply is doubled,what should be the values of inductance $L$ and capacitance $C$ to maintain the same current?