Answer the following questions :
(a) In any a.c. circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages acorss the series elements of the circuit ? Is the same true for r.m.s. voltage?
(b) A capacitor is used in the primary circuit of an induction coil.
(c ) An applied voltage signal consists of a superposition of a d.c. voltage and an a.c. voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the d.c. signal will appear across C and the a.c. signal will appear across L.
(d) A choke coil in series with a lamp is connected to a d.c. 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 observation if the connection is to an a.c. line.
(e) Why is choke coil needed in use of fluorescent tubes with ac mains ? Why can we not use an ordinary resistor instead of choke coil?

Explanation

(a) Yes, applied instantaneous voltages is always equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit.
No, this is not ture in case of r.m.s. voltages, because such voltages across different elements may not be in same phase.
(b) When the circuit is broken, the large induced voltage is used up in charging the capacitor. Thus sparking etc. is avoided.
(c ) We know, `X_(L) = omega L = 2 pi v L`
`X_(C ) = (1)/(omega C) = (1)/(2 pi v C)`.
For d.c., `v = 0, X_(C ) = oo` The capacitor blocks d.c. signal appears acorss C.
For a.c. of high freq. `X_(L) rarr` very large.
`:.` Inductor blocks it, Hence a.c. signal appears across L.
(d) On a d.c. line, choke has no impedance. Therefore, lamp shines brightly and there is no effect of intserting iron core in the choke. On an a.c. line, choke offers impedence. So the bulb lights dimly. When an iron core is inserted in the choke, its impedance to a.c. increases further. Therefore, brightness of the bulb decreases.
(e) A choke coil is needed in the use of fluorescent tubes to reduce ac without loss of power. If we use an ordinary resistor, ac will reduce, but loss of power due to heating will be there.
Power dissipated/cycle `= E_(v) I_(v) cos phi`
In a resistor, `phi = 0^(@)` `:.` Power dissipated/cycle `= E_(v) I_(v) cos 0^(@) = E_(v) I_(v) = max`
In a choke coil, `phi = 90^(@)` `:.` Power dissipated/cycle `= E_(v) I_(v) cos 90^(@) =` zero