Calculate the capacitive reactance of a power inserter's capacitor at 60 Hz with a capacitance of 1,000 pF. What is the reactance?

To find the capacitive reactance, you can use the formula:

[ X_C = \frac{1}{2 \pi f C} ]

where:

• ( X_C ) is the capacitive reactance in ohms,

• ( f ) is the frequency in hertz,

• ( C ) is the capacitance in farads.

First, convert the capacitance from picofarads to farads:

[ C = 1,000 , \text{pF} = 1,000 \times 10^{-12} , \text{F} = 1 \times 10^{-9} , \text{F} ]

Next, insert the values into the formula. The frequency is given as 60 Hz:

[ X_C = \frac{1}{2 \pi (60) (1 \times 10^{-9})} ]

Calculating the denominator:

[ 2 \pi \times 60 \approx 376.99 ]

Now substituting this back into the equation gives:

[ X_C = \frac{1}{376.99 \times 10^{-9}} ]

[ X_C \approx \frac{1}{3