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 voltage is equal to the alebraic sum of the instantaneous voltage across is not true for rms voltage because voltage across different elements may not be in phase.
(b) Acapacitor is used in the primary circuit because when the circuit is broken , the large induced voltage is used for charging the capacitor, thus prevents sparks .
(c) for DC supply, reactance offered by inductor is negligible as `X_(L) = omega_(L) = 0 ( omega = 0 "for DC ")` and that offered by capacitor is infinite as `X_(C) = 1//omega C = infty`, so, the DC signal appears across C. For high frequency AC source , reactance offered by inductor is very high (almost infinite) and that offered by capacitor is very low (almost zero) . so, the AC signal appears across inductor.
(d) For steady-state DC source, inductance L has no effect as `omega` = 0 for DC, and hence reactance, offered by inductor , `X_(L) = omega` L = 0. Even when L is increased by inserting an iron core in the choke coil, the impedance `X_(L)` will still remain zero. For AC source the lamp will shine dimly because of additional impedance of the choke. It will dim further when the iron core is inserted which increases the choke.s impedance.
(e) A choke coil reduces voltage the tube without wasting power. On the other hand, a resistor would waste power in the form of heat.