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Answer :
The capacitive reactance of capasitor is 0.004 Ω or 4 × 10⁻³ Ω.
When AC (alternating current) passes through a capacitor, the current will be limited by the internal impedance of the capacitor. This is known as capacitive reactance. The formula
[tex]X_c \:=\: \frac{1}{2 \pi \times f \times C}[/tex]
Because [tex]\omega \:=\: 2 \pi \times f[/tex]
[tex]X_c \:=\: \frac{1}{\omega \times C}[/tex]
- C = capacitance (Farad)
- f = frequency (Hertz)
- π = 3.14 or [tex]\frac{22}{7}[/tex]
- ω = angular frequency (radians/s)
- [tex]X_C[/tex] = capacitive reactance (Ω)
From the problems
- C = 0.5 Farad
- V = 6 Volt
- ω = 500 radians/s
[tex]X_c \:=\: \frac{1}{\omega \times C}[/tex]
[tex]X_c \:=\: \frac{1}{500 \times 0.5}[/tex]
[tex]X_c \:=\: \frac{1}{250}[/tex]
[tex]X_c[/tex] = 0.004 Ω
[tex]X_c \:=\: 4 \times 10^{- 3}[/tex] Ω
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