$A$ series $RLC$ circuit is shown here. The source frequency $f$ is varied, but the current is kept unchanged. Which of the curves showing changes of $V_C$ and $V_L$ with frequency would be valid for the circuit under consideration?

Answer the following questions:
$(a)$ In any $ac$ circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? Is the same true for $rms$ voltage?
$(b)$ Why is a capacitor used in the primary circuit of an induction coil?
$(c)$ An applied voltage signal consists of a superposition of a $dc$ voltage and an $ac$ voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the $dc$ signal will appear across $C$ and the $ac$ signal across $L$.
$(d)$ $A$ choke coil in series with a lamp is connected to a $dc$ line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamp's brightness. Predict the corresponding observations if the connection is to an $ac$ line.
$(e)$ Why is a choke coil needed in the use of fluorescent tubes with $ac$ mains? Why can we not use an ordinary resistor instead of the choke coil?

An alternating power supply of $220 \,V$ is applied across a series circuit of resistance $10 \sqrt{3} \,\Omega$,capacitive reactance $40 \,\Omega$,and inductive reactance $30 \,\Omega$. The respective currents in the circuit for zero and infinite frequencies are

$A$ $ 100 \,W $ bulb is connected to an $ AC $ source of $ 220 \,V, 50 \,Hz $. Then the current flowing through the bulb is

$A$ direct current of $4\,A$ and an alternating current of peak value $4\,A$ flow through resistances of $3\,\Omega$ and $2\,\Omega$ respectively. The ratio of heat produced in the two resistances in the same interval of time will be.

$A$ $100 \, \Omega$ resistance and a capacitor of $100 \, \Omega$ reactance are connected in series across a $220 \, V$ source. When the capacitor is $50\%$ charged,the peak value of the displacement current is.....$A$