A capacitor has a capacitance of 5 µF connected to a 240 V circuit. What is the expected current at 60 Hz?

To determine the current flowing through a capacitor in an AC circuit, you can use the formula for capacitive reactance and the relationship between voltage and current in an AC circuit. The capacitive reactance (Xc) is given by 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 (5 µF or ( 5 \times 10^{-6} ) F).

First, calculate the capacitive reactance:

1. Convert capacitance from microfarads to farads:

[ C = 5 \times 10^{-6} , \text{F} ]

2. Substitute the values into the formula:

[ X_c = \frac{1}{2 \pi (60) (5 \times 10^{-6})} ]

Calculating this gives:

[ X_c \approx \frac{1}{2 \pi (60)(5 \times 10^{-6})} \approx 530.53 , \Omega ]

Next, we can find the current