What is the total capacitive reactance for two capacitors of 20 µF and 30 µF connected in series at 60 Hz?

To calculate the total capacitive reactance for two capacitors connected in series, you need to begin by determining the individual capacitive reactances and then apply the formula for capacitors in series.

The capacitive reactance (Xc) can be calculated with the formula:

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

where:

• ( f ) is the frequency in hertz (60 Hz in this case),

• ( C ) is the capacitance in farads.

First, you should convert the capacitances from microfarads to farads:

• 20 µF = 20 × 10^-6 F = 0.000020 F

• 30 µF = 30 × 10^-6 F = 0.000030 F

Now, calculate the individual capacitive reactances for each capacitor:

For the 20 µF capacitor:

[ X_{c1} = \frac{1}{2\pi (60)(20 \times 10^{-6})} ]

Calculating this gives:

[ X_{c1} \approx 132.63 , \Omega ]

For the 30 µF capacitor:

[ X_{c