In an $AC$ circuit,an inductor,a capacitor,and a resistor are connected in series with $X_{L} = R = X_{C}$. The impedance of this circuit is:

$A$ series $LCR$ circuit containing a resistance of $120 \, \Omega$ has an angular resonance frequency of $4 \times 10^3 \, rad \, s^{-1}.$ At resonance, the voltages across the resistance and the inductance are $60 \, V$ and $40 \, V$ respectively. The values of $L$ and $C$ are respectively:

In the given series $LCR$ circuit,if the value of $R$ is changed,then:

$A$ series $LR$ circuit is connected to an ac source of frequency $\omega$ and the inductive reactance is equal to $2R$. $A$ capacitance of capacitive reactance equal to $R$ is added in series with $L$ and $R$. The ratio of the new power factor to the old one is

$A$ resistor of resistance $40 \Omega$,a capacitor of capacitive reactance $20 \Omega$,and an inductor of inductive reactance $50 \Omega$ are connected in series to an $ac$ source of $100 \ V$. The current through the circuit is (in $A$)

$A$ capacitor and an inductance coil are connected in separate $AC$ circuits with a bulb glowing in both the circuits. The bulb glows more brightly when