Three capacitors, a 12 µF, a 20 µF, and a 30 µF, are connected in series to a 400 Hz source. The total XC is:

Three capacitors, a 12 µF, a 20 µF, and a 30 µF, are connected in series to a 400 Hz source. The total XC is:

• A. 6.42 ohms
• B. 42.78 ohms
• C. 442.09 ohms
• D. 66.32 ohms

Answer: (D)

To determine the total capacitive reactance (XC) of capacitors connected in series, you first need to calculate the individual capacitive reactance of each capacitor and then apply the formula for capacitors in series. The formula for the capacitive reactance of an individual capacitor is: \[ X_C = \frac{1}{2\pi f C} \] where \( f \) is the frequency in hertz and \( C \) is the capacitance in farads. For the three capacitors given, you will calculate the reactance for each: 1. For the 12 µF capacitor: \[ X_{C1} = \frac{1}{2\pi \times 400 \times 12 \times 10^{-6}} \approx 33.18 \text{ ohms} \] 2. For the 20 µF capacitor: \[ X_{C2} = \frac{1}{2\pi \times 400 \times 20 \times 10^{-6}} \approx 19.89 \text{ ohms} \] 3. For the 30 µF capacitor: \[ X_{C3} = \frac{1

To determine the total capacitive reactance (XC) of capacitors connected in series, you first need to calculate the individual capacitive reactance of each capacitor and then apply the formula for capacitors in series.

The formula for the capacitive reactance of an individual capacitor is:

[

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

]

where ( f ) is the frequency in hertz and ( C ) is the capacitance in farads.

For the three capacitors given, you will calculate the reactance for each:

1. For the 12 µF capacitor:

[

X_{C1} = \frac{1}{2\pi \times 400 \times 12 \times 10^{-6}} \approx 33.18 \text{ ohms}

]

2. For the 20 µF capacitor:

[

X_{C2} = \frac{1}{2\pi \times 400 \times 20 \times 10^{-6}} \approx 19.89 \text{ ohms}

]

3. For the 30 µF capacitor:

[

X_{C3} = \frac{1