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An AC source of angular frequency ω is connected across a series combination of a resistor r and a capacitor C. The circuit current is I. If the source frequency is reduced to ω/3 while the applied voltage amplitude remains unchanged, the current becomes I/2. The ratio of capacitive reactance to resistance at the original frequency ω is
- √(3/5)
- √(2/5)
- √(1/5)
- √(4/5)
Correct answer: √(3/5)
Solution
At w/3, Xc triples. I/2 = V/sqrt(r^2 + 9Xc^2) with I = V/sqrt(r^2 + Xc^2) gives r^2 + 9Xc^2 = 4(r^2 + Xc^2) -> 5Xc^2 = 3r^2 -> Xc/r = sqrt(3/5).
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