39.5k views
5 votes
Suppose an AC source with an rms voltsge of 480 V and a frequency of 58.5 Hz is connected to a 26.5 uF capacitor. What rms current, in amps, flows through this circuit? What could be the rms current be, in amps, if we changed the source frequency to 0.15 kHz?

1 Answer

4 votes

Final answer:

The rms current flowing through the circuit can be calculated using the formula Irms = Vrms/Xc, where Vrms is the rms voltage and Xc is the capacitive reactance. The rms current is 4.28 A for a frequency of 58.5 Hz and 54.05 A for a frequency of 0.15 kHz.

Step-by-step explanation:

To find the rms current flowing through the circuit, we need to calculate the capacitive reactance first. The formula for capacitive reactance is given by Xc = 1/(2πfC), where Xc is the capacitive reactance, f is the frequency, and C is the capacitance.

Using the given values, at a frequency of 58.5 Hz and a capacitance of 26.5 uF, we can calculate Xc as follows:

Xc = 1/(2π * 58.5 * 26.5 * 10^-6) = 112.15 Ω

The rms current, Irms, can be calculated using the formula Irms = Vrms/Xc, where Vrms is the rms voltage of the AC source:

Irms = 480 V / 112.15 Ω = 4.28 A

If we change the source frequency to 0.15 kHz (150 Hz), we can calculate the new capacitive reactance and rms current using the same formulas:

Xc = 1/(2π * 150 * 26.5 * 10^-6) = 8.89 Ω

Irms = 480 V / 8.89 Ω = 54.05 A

User Vaultah
by
7.6k points