Question

Suppose an AC source with an rms voltage of 480 V and a frequency of 62.5 Hz is connected to a 27μF capacitor.

What rms current, in amps, flows through this circuit?

Answer 1

To calculate the rms current in the circuit, first calculate the reactance of the capacitor using the given formula. Then, use Ohm's law to find the rms current. The rms current is approximately 4.02 amps.

Step-by-step explanation:

To determine the rms current flowing through the circuit, we need to calculate the reactance and then use Ohm's Law. The reactance of a capacitor in an AC circuit can be calculated using the formula:

Xc = 1 / (2πfC)

Where Xc is the reactance, f is the frequency in hertz, and C is the capacitance in farads.

For the given circuit:

Xc = 1 / (2π x 62.5 x 27 x 10^-6) ≈ 119.5 ohms

Using Ohm's Law, we can calculate the rms current (I) using the formula:

I = Vrms / Xc

Where Vrms is the rms voltage.

For the given circuit:

I = 480 / 119.5 ≈ 4.02 amps