What is the capacitive reactance in ohms for a 60 Hz circuit containing a 12 µF capacitor after converting microfarads to farads?

To calculate 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, and ( C ) is the capacitance in farads.

First, convert the capacitance from microfarads to farads. Since 1 microfarad (µF) is equal to ( 10^{-6} ) farads:

[

12 , \mu F = 12 \times 10^{-6} F = 0.000012 F

]

Now, plug the values into the formula. The frequency ( f ) is 60 Hz, and the capacitance ( C ) is 0.000012 F.

Calculating ( X_c ):

[

X_c = \frac{1}{2 \pi (60) (0.000012)}

]

Calculating the denominator:

[

2 \pi (60) (0.000012) \approx 0.004523

]

Thus,

[

X_c \approx \frac{1}{