Derive an expression for the impedance of a series LCR circuit connected to an AC supply of variable frequency.
Plot a graph showing variation of current with the frequency of the applied voltage.
Explain briefly how the phenomenon of resonance in the circuit can be used in the
Tuning mechanism of a radio or a TV set.a)
Expression for impedance in LCR series circuit:
Suppose a resistance R, inductance L and capacitance C are connected to series and an alternating voltage V = is applied across it.
Thus, VR and (VC -VL) are mutually perpendicular and the phase difference between them is 90°. As seen in the fig, we can say that, as applied voltage across the circuit is V, the resultant of VR and (VC -VL) will also be V.
So,
Therefore, Impedance of the circuit is given by,
This is the impedence of the LCR series circuit.
b)
The below graph shows the variation of current with the frequency of the applied voltage.
c)
A radio or a TV set has a L-C circuit with capacitor of variable capacitance C. The circuit remains connected with an aerial coil through the phenomenon of mutual inductance. Suppose a radio or TV station is transmitted a programme at frequency f, then waves produce alternating voltage of frequency f, in area, due to which an emf of same frequency is induced in LC circuit, When capacitor C is in circuit is varied then for a particular value of capacitance, , the resonance occurs and maximum current flows in the circuit; so the radio or TV gets tuned.