An inductor of inductance 150 μH is connected in parallel with a variable capacitor whose capacitance can be changed from 500 pF to 20 pF. Calculate the maximum frequency and minimum frequency for which the circuit can be tuned. (Ans : 2.91 MHz, 0.58 MHz)
Data Given:
Inductance = L = 150 μH = 150 x10⁻⁶ H
Capacitance Maximum = Cmax = 500 pF = 500 x10⁻¹² F
Capacitance Minimum = Cmin = 20 pF = 20 x10⁻¹² F
To Find:
(i) Frequency Maximum = fmax = ?
(ii) Frequency Minimum = fmin = ?
Solution:
(i) Frequency Maximum = fmax = ?
We know that
fmax = 12ㄫ√LCmin
By putting values
fmax = 12x3.1415√150x10⁻⁶Hx20x10⁻¹²F
fmax = 16.283√3000x10⁻¹⁸s²
fmax = 16.283x54.772x10⁻⁹s
fmax = 1344.132476x10⁻⁹s
fmax = 0.00291x 10⁹ s⁻¹
or
fmax= 2.91x 10⁶ Hz
or
fmax = 2.91 MHz -----------------Ans.1
(ii) Frequency Minimum = fmin = ?
We know that
fmin = 12ㄫ√LCmax
By putting values
fmin = 12x3.1415√150x10⁻⁶Hx500x10⁻¹²F
fmin = 16.283√75,000x10⁻¹⁸s²
fmin = 16.283x273.861x10⁻⁹s
fmin = 11720.668663x10⁻⁹s
fmin= 0.000581x 10⁹ s⁻¹
or
fmin = 0.581x 10⁶ Hz
or
fmin = 0.581 MHz -----------------Ans.2
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