In an $LCR$ circuit,the capacitance is changed from $C$ to $4C$. For the same resonant frequency,the inductance should be changed from $L$ to:

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 $= 10 \sqrt{2} \ V$

Write the differential equation of charge for $L-C-R$ series $AC$ circuit.

Obtain the relation of phase between instantaneous current and voltage with the help of a phasor diagram for a series $LCR$ circuit.

When a capacitor is connected in series with an $LR$ circuit,the alternating current flowing in the circuit

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 $\,V$)