When the frequency of the oscillator in a series RLC circuit is doubled:
Correct answer: B. The capacitive reactance is halved
- A. The capacitive reactance is doubled
- B. The capacitive reactance is halved
- C. The impedance is doubled
- D. The current amplitude is halved
Explanation
The capacitive reactance ((X_C)) in a series RLC circuit is given by the formula:[ X_C = frac{1}{2pi f C} ]where ( f ) is the frequency and ( C ) is the capacitance.When the frequency ((f)) is doubled, the capacitive reactance is halved:[ X_C' = frac{1}{2pi (2f) C} = frac{1}{4pi f C} = frac{1}{2} X_C ]Explanations for Wrong Choices:- (a) The capacitive reactance is doubled: This is incorrect. As explained above, the capacitive reactance is halved when the frequency is doubled.- (c) The impedance is doubled: This is not correct. The impedance is affected by changes in both resistive and reactive components, not just the capacitive reactance.- (d) The current amplitude is halved: This is incorrect. Changes in frequency affect reactances, not the amplitude of the current directly.So, the correct answer is (b) The capacitive reactance is halved.
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