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 = 12LCmin

By putting values

fmax = 123.141515010H2010¹²F

fmax = 16.283300010¹s²

fmax = 16.28354.77210s

fmax = 1344.13247610s

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 = 12LCmax

By putting values

fmin = 123.141515010H50010¹²F

fmin = 16.28375,00010¹s²

fmin = 16.283273.86110s

fmin = 11720.66866310s

fmin= 0.000581x 10⁹ s⁻¹

or

fmin = 0.581x 10⁶ Hz

or


fmin = 0.581 MHz -----------------Ans.2



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