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?

In the circuit shown below, the ac source has voltage $V = 30 \cos(\omega t) \text{ V}$ with $\omega = 2000 \text{ rad/s}$. What will be the amplitude of the current?

When $L$, $C$, and $R$ are connected in series with an $AC$ source of frequency $f$, the current leads the voltage by a phase angle of $45^{\circ}$. What is the value of $C$?

An inductor coil takes a current of $8 \, A$ when connected to a $100 \, V$ and $50 \, Hz$ $AC$ source. $A$ pure resistor under the same condition takes a current of $10 \, A$. If the inductor coil and resistor are connected in series to a $100 \, V$ and $40 \, Hz$ $AC$ supply, then the current in the series combination of the above resistor and inductor is:

How does the sign of the phase angle $\phi$,by which the supply voltage leads the current in an $LCR$ series circuit,change as the supply frequency is gradually increased from very low to very high values?

$A$ circuit has three elements: a resistance of $11 \Omega$,a coil of inductive reactance $120 \Omega$,and a capacitive reactance of $120 \Omega$ in series,connected to an $A.C.$ source of $110 \, V, 60 \, Hz$. Which of the three elements has the minimum potential difference?