An LC circuit oscillates at a frequency of 2.50×103 Hz. What will the frequency be if the inductance is halved? 1.77×103 Hz 5.00×103 Hz 1.25×103 Hz 3.54×103 Hz
Question
An LC circuit oscillates at a frequency of 2.50×10³ Hz. What will the frequency be if the inductance is halved?
- 1.77×10³ Hz
- 5.00×10³ Hz
- 1.25×10³ Hz
- 3.54×10³ Hz
Solution
The frequency of oscillation in an LC circuit is given by the formula:
f = 1 / (2π√(LC))
where: f is the frequency, L is the inductance, and C is the capacitance.
If the inductance is halved, the new frequency (f') will be:
f' = 1 / (2π√((L/2)C))
Simplifying this gives:
f' = 1 / (2π√(LC/2))
Comparing this with the original formula, we can see that the new frequency is the original frequency multiplied by the square root of 2. Therefore, if the original frequency was 2.50×10^3 Hz, the new frequency will be:
f' = 2.50×10^3 Hz * √2 ≈ 3.54×10^3 Hz
So, the correct answer is 3.54×10^3 Hz.
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