A variable capacitor with a range from 10 to 365 pF is used with a coil to form

Question

A variable capacitor with a range from 10 to 365 pF is used with a coil to form a variablefrequency LC circuit to tune the input to a radio. (a) What ratio of maximum to minimum frequencies may be tuned with such a capacitor? If this capacitor is to tune from 0.54 to 1.60 MHz, the ratio computed in (a) is too large. By adding a capacitor in parallel to the variable capacitor this range may be adjusted. How large should this capacitor be and what inductance should be chosen in order to tune the desired range of frequencies?

Explanation / Answer

given data

capacitor range = 10-365 pF

frequency = 0.54--1.60 Hz

= 1 / L C

where C------max

a) Cmin = 36.5 ( 365 / 10)
= 1 / L * 36.5 = 6.0415
ratio of max frequency to min frequency 6.0415

How large should this capacitor be and what inductance should be chosen in order to tune the desired range of frequencies?

b) 1.6 / 0.54 = 2.963
C max / C min = 2.963 ^2 = 8.779
What capacitance should be added
(365+ x ) / (10 + x ) = 8.779

x = 35.635 pF

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