If a 35 microfarad capacitor is connected to a 120 volt, 60 Hz line, what is the value of Xc?

To find the capacitive reactance (Xc) of a capacitor in an AC circuit, the formula used is:

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

where:

• ( f ) is the frequency in hertz (Hz),

• ( C ) is the capacitance in farads (F).

In this case, the capacitance provided is 35 microfarads (or ( 35 \times 10^{-6} , F)), and the frequency is 60 Hz.

First, we convert the capacitance:

[ C = 35 \times 10^{-6} , F = 0.000035 , F ]

Now we can substitute the values into the formula:

1. Calculate the product ( 2\pi f ):

[ 2\pi f = 2 \times \pi \times 60 \approx 376.99 ]

2. Now, substitute this and the capacitance into the Xc formula:

[ Xc = \frac{1}{376.99 \times 0.000035} ]

3. Performing this calculation:

[ Xc \approx \frac{1}{0.