Question

What is the capacitive reactance of a capacitor of 5µF at a frequency of (1) 50 Hz and (2) 20KHZ? 

Answer 1

Given:

C = 5 μF = 5 × 10^-6 F
f₁ = 50 Hz, f₂ = 20 kHz

To find:

1. Capacitive reactance at 50 Hz (`"X"_"C"""_1`)
2. Capacitive reactance at 20 kHz (`"X"_"C"""_2`)  

Formula: `"X"_"C" = 1/(2pi"fC")`

Calculation: 

1. 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
2. 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 

1. When the frequency is 50 Hz, the capacitive reactance is 636.94 Ω.
2. When the frequency is 20 kHz, the capacitive reactance is 1.59 Ω.