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Which of the following coil will have large resonant frequency?
Answer & Solution
Correct Answer:
Option
D
Resonant Frequency: The resonant frequency of a coil in an AC circuit is determined by both its inductance and capacitance. It is given by the formula:
$$f_r = \frac{1}{2 \pi \sqrt{L C}}$$
where $$f_r$$ is the resonant frequency,
Effect of Capacitance: From the formula, it is clear that the resonant frequency is inversely proportional to the square root of the capacitance. Therefore, a lower capacitance results in a higher resonant frequency.
Options Analysis:
Therefore, the coil with low distributed capacitance will have a large resonant frequency.
$$f_r = \frac{1}{2 \pi \sqrt{L C}}$$
where $$f_r$$ is the resonant frequency,
L is the inductance, and C is the capacitance.
Effect of Capacitance: From the formula, it is clear that the resonant frequency is inversely proportional to the square root of the capacitance. Therefore, a lower capacitance results in a higher resonant frequency.
Options Analysis:
Option A: A coil with large resistance - The resistance of the coil does not directly affect the resonant frequency.
Option B: A coil with low resistance - Similar to option A, resistance does not directly impact the resonant frequency.
Option C: A coil with large distributed capacitance - Larger capacitance results in a lower resonant frequency.
Option D: A coil with low distributed capacitance - Lower capacitance results in a higher resonant frequency.
Therefore, the coil with low distributed capacitance will have a large resonant frequency.
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LoginAs per theory , resonant frequency is inversely proportional to √(LC)
w = 1/√LC. C should be low than resonant frequency will be high.