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Solved Problems-13

Problems-13
A coil of inductance L and resistance R, in series with a capacitor is supplied at a constant voltage from a variable frequency source. Find the values of that frequency, in terms of RL and ω0 at which the circuit current would be half as much as at resonance. Hence, or otherwise, determine the bandwidth and selectivity of the circuit.
Solution
The current at resonance is,
 
Description: 4072.png
 
and current at any other frequency is,
 
Description: 4078.png
 
For this problem,
 
Description: 4084.png
 
Description: 4090.png
⇒ Description: 4096.png
 
⇒ 3 = Description: 4102.png
 
⇒ 3 = Description: 4108.png
 
Description: 4114.png
 
Description: 4120.png
 
⇒ Description: 4126.png
 
If the two frequencies are ω2 and ω1, (ω2 > ω0 > ω1) then,
Description: 4134.png
and
 
⇒ Description: 4144.png
 
Description: 4155.png
 
Alternately,
Description: 4163.png
 
⇒ Description: 4169.png
 
Therefore, Description: 4175.png
 
Taking the positive roots of ω,
 
Description: 4182.png
 
∴ Bandwidth Description: 4189.png
 




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