If the capacitance of an L-C circuit is made four times, then the frequency of the circuit becomes:
Correct answer: B. One-half
- A. Twice
- B. One-half
- C. Four times
- D. None
Explanation
The resonant frequency ((f_0)) of a series L-C circuit is inversely proportional to the square root of the product of inductance (L) and capacitance (C). The formula is:[ f_0 = frac{1}{2pi sqrt{LC}} ]If the capacitance (C) is made four times, the new resonant frequency ((f')) can be expressed as:[ f' = frac{1}{2pi sqrt{L cdot 4C}} = frac{1}{2pi cdot 2 sqrt{LC}} = frac{1}{4pi sqrt{LC}} ]Comparing this with the original frequency ((f_0)), we can see that the new frequency is one-half of the original frequency.So, the correct answer is (b) One-half.
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