An inductor L of inductance XL is connected in series with a bulb B and an ac source.
How would brightness of the bulb change when (i) number of turn in the inductor is reduced, (ii) an iron rod is inserted in the inductor and (iii) a capacitor of reactance XC = XL is inserted in series in the circuit. Justify your answer in each case.i) Net resistance in the circuit is given by, 
Inductance is given by, 
As the number of turns decreases, L decreases.
Inductance is given by, 
Therefore, 
will also decrease thereby, reducing the net resistance in the circuit. Thus, current increases and the brightness of the bulb is increased.
ii) When a soft iron rod is inserted into the circuit, L increases. Therefore, inductive reactance also increases. Net resistance increases and the flow of current in the circuit decreases. Thus, the brightness of the bulb will decrease.
iii) When a capacitor of reactance XL = XC is connected in series with the circuit net resistance becomes,
; where R is the resistance of the bulb.
Here, we will have Z= R which is the condition of resonance.
At resonance, maximum current will flow through the circuit. Therefore, the brightness of the bulb will increase.
The resistance offered by the capacitor when connected to an electrical circuit is known as capacitive reactance.
It is given by,
where, 
is the angular frequency of the source, and
C, is the capacitance of the capacitor.
SI Unit is ohm.
In the circuit shown below, the switch is kept in position a for a long time and is then thrown to position b. The amplitude of the resulting oscillating current is given by
E / R
infinity
D.
When switch is in position a, then capacitor will be charged, such that
Charge on capacitor, q = CE
Energy stored in capacitor, U = q2 / 2C
When switch is in position b, then circuit becomes an LC oscillator.
Let amplitude of current in LC circuit be I0. From conservation of energy,
Maximum electrical energy = Maximum magnetic energy
The carrier wave is given by C (t) = 2sin (8πt) Volt.
The modulating signal is a square wave as shown. Find modulation index. 
The generalized equation of a carrier wave is given by, 
The generalized equation of a modulating signal is given by,
On comparing the given equation of carrier wave with the generalized equation, we get,
Amplitude of modulating signal, Am = 1 V
Amplitude of carrier wave, Ac = 2 V
Modulation index is the ratio of the amplitude of the modulating signal to the amplitude of carrier wave 
.
It is denoted by,
So, 
Switch
