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Question
What is the capacitive reactance of a capacitor of 5µF at a frequency of (1) 50 Hz and (2) 20KHZ?
Solution
Given:
C = 5 μF = 5 × 10-6 F
f1 = 50 Hz, f2 = 20 kHz
To find:
- Capacitive reactance at 50 Hz (`"X"_"C"""_1`)
- Capacitive reactance at 20 kHz (`"X"_"C"""_2`)
Formula: `"X"_"C" = 1/(2pi"fC")`
Calculation:
- From formula,
`"X"_"C"""_1 = 1/(2pi"f"_1"C")`
= `1/(2 xx 3.142 xx 50 xx 5 xx 10^-6)`
= 636.94 Ω - From formula,
`"X"_"C"""_2 = 1/(2pi"f"_2"C")`
= `1/(2 xx 3.142 xx 20 xx 10^3 xx 5 xx 10^-6)`
= 1.59 Ω
- When the frequency is 50 Hz, the capacitive reactance is 636.94 Ω.
- When the frequency is 20 kHz, the capacitive reactance is 1.59 Ω.
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