Question

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) A capacitor is 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 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?

Answer 1

(a) Yes, the algebraic sum of instantaneous voltages across the circuit elements equals the instantaneous value of applied voltage. The simple sum of the voltages does not add up to the applied voltage but the vector sum does. (b) When the circuit is broken, there is a large induced emf due to the change in magnetic field linked with coil as the current changes. This back emf can cause sparking at the switch. The capacitor stores the charge and helps prevent sparking. (c) The dc signal appears across C because it offers an infinite impedance as = =
c
1
X and 0
C
ω
ω . The ac signal appears across L because it offers a very large resistance as =
X L and is given to be very high. L ω ω (d) In case of an ac line the brightness of the bulb will decrease. Introducing a choke increases the impedance of the inductor. So the current in the circuit decreases. Note that this is because the value of inductance depends on permeability than air.