Question

The graph below shows the variation in current flowing through two LCR circuits used in radios P and Q, with the change in frequency. To prevent adjacentchannel interference while tuning the radio to a particular frequency it is desirable that the frequency of adjacent channels does not lie in the bandwidth region of the selected frequency. 

(a) Which radio will allow a person to hear a radio channel of frequency f_o, without the interference of other frequencies? Give reason. 

(Assume f₁, f_o and f₂ are the only radio frequencies available and to prevent adjacent-channel interference on the band) 

(b) Compare the resistance and capacitance of LCR circuit used in radios P and Q, if both the circuits have the same inductance. Give reason.

Answer 1

(a) Radio P will allow the person to hear the radio channel of frequency fo, without the interference of other frequencies. 

Both f₁ and f₂ do not lie in the bandwidth of the radio P while frequency f1 lies in the bandwidth of radio Q.

(b) The maximum current at resonance in an LCR circuit is given by 

i_max = V/R

Since i_P > i_Q, the resistance of circuit used in radio P is less than the resistance of the circuit used in radio Q. 

The resonance frequency f_o = 1/(2π√LC) 

As L and f_o is the same for both circuits the capacitance of both circuits will be the same.