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Q.

The resonant frequency of the L-C circuit is f₀before insertion of the dielectric of $ε$ _r = 4 . After inserting the dielectric, the resonant frequency will be:

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a

$\frac{f_{0}}{4}$

b

$\frac{f_{0}}{2}$

c

4f₀

d

2f₀

answer is A.

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Detailed Solution

Resonant frequency of LC circuit is $f_{0} = \frac{1}{2 π \sqrt{LC}} o n i n s e r t i n g a d i e l e c t r i c c a p a c i \tan c e i n c r e a s e s b y ε_{r} (= 4) t i m e s, n o w t h e n e w f r e q u e n c y i s f = \frac{1}{2 π \sqrt{L 4 C}} = \frac{f_{0}}{2}$

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The resonant frequency of the L-C circuit is f0 before insertion of the dielectric of εr = 4 . After inserting the dielectric, the resonant frequency will be: