Coupon Accepted Successfully!


Solved 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.
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
⇒ Description: 4144.png
Description: 4155.png
Description: 4163.png
⇒ Description: 4169.png
Therefore, Description: 4175.png
Taking the positive roots of ω,
Description: 4182.png
∴ Bandwidth Description: 4189.png

Test Your Skills Now!
Take a Quiz now
Reviewer Name