Answer :
Final answer:
In an RLC series circuit, if the frequency increases by 5 times the resonant frequency, the inductive reactance and impedance also increase by the same factor, making the ratio of the inductive reactance at 5 times the resonant frequency to that at resonant frequency 5:1.
Explanation:
In an RLC series circuit, we have resonance when the frequency of the source matches the natural frequency of the circuit. At resonant frequency, the inductive reactance cancels out the capacitive reactance, making the circuit purely resistive (i.e., impedance equals the resistance).
When the frequency becomes 5 times the resonant frequency, the statement suggests that the impedance increases 5 times. This implies that the increase in impedance is due to the inductive reactance. From the formula for inductive reactance XL = 2πfL, it can be deduced that the inductive reactance is directly proportional to the frequency.
So, when the frequency is multiplied by 5, the inductive reactance (and therefore the impedance) would also increase 5 times i.e., the ratios of the inductive reactance at 5 times the resonant frequency to that at resonant frequency is 5:1.
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