For a 50 Hz circuit with a 25 µF capacitor, what is the capacitive reactance in ohms after conversion?

To determine the capacitive reactance of a capacitor in a circuit, the formula used is:

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

where:

• ( X_C ) is the capacitive reactance in ohms,

• ( f ) is the frequency of the circuit in hertz (Hz), and

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

In this scenario, the frequency ( f ) is 50 Hz and the capacitance ( C ) is 25 µF, which is equal to ( 25 \times 10^{-6} ) F. Now, we can substitute these values into the formula:

1. Calculate ( 2 \pi f ):

• ( 2 \pi (50) = 314.16 ) (approximately)

2. Now, use this to calculate ( X_C ):

• ( X_C = \frac{1}{314.16 \times 25 \times 10^{-6}} )

3. Calculate the denominator:

• ( 314.16 \times 25 \times 10^{-6} = 0.007854 )