Calculating Capacitive Reactance and then Current

The capacitive reactance is found directly from the expression in $X_C=\frac{1}{\mathrm{2\pi }\text{fC}}$. Once $X_C$ has been found at each frequency, Ohm’s law stated as $I=V/X_C$ can be used to find the current at each frequency.

Entering the frequency and capacitance into $X_C=\frac{1}{\mathrm{2\pi }\text{fC}}$ gives

Similarly, at 10 kHz,

The rms current is now found using the version of Ohm’s law in $I=V/X_C$, given the applied rms voltage is 120 V. For the first frequency, this yields

Similarly, at 10 kHz,

The capacitor reacts very differently at the two different frequencies, and in exactly the opposite way an inductor reacts. At the higher frequency, its reactance is small and the current is large. Capacitors favor change, whereas inductors oppose change. Capacitors impede low frequencies the most, since low frequency allows them time to become charged and stop the current. Capacitors can be used to filter out low frequencies. For example, a capacitor in series with a sound reproduction system rids it of the 60 Hz hum.