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Question
A 15.0 μF capacitor is connected to a 220 V, 50 Hz source. Find the capacitive reactance and the current (rms and peak) in the circuit. If the frequency is doubled, what will happen to the capacitive reactance and the current?
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Solution
Data: C= 15 µF = 15 x 10-6 F, Vrms = 220 V, f = 50 Hz,
The capacitive reactance = `1/(2pi"fC")`
`= 1/(2(3.142)(50)(15 xx 10^-6)) = (100xx100)/((3.142)(15))`
= 212.2 Ω
`"i"_"rms" = "V"_"rms"/"capacitive reactance" = 220/212.2` = 1.037 A
`"i"_"peak" = "i"_"rms" sqrt2 = (1.037)(1.414) = 1.466`A
If the frequency is doubled, the capacitive reactance will be halved and the current will be doubled.
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