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When dealing with capacitors in series, it's critical to understand how equivalent capacitance is calculated. Unlike resistors where you simply add up their values for a series connection, capacitors in series behave a bit differently. The formula used for finding the equivalent capacitance \( C_{eq} \) is \( \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \ldots + \frac{1}{C_n} \). Here, \( C_1 \) and \( C_2 \) are the capacitance values of the capacitors in series.

For our specific problem, we have a \( 4.40-\mu F \) and an \( 8.80-\mu F \) capacitor. Substituting these into the formula gives \( \frac{1}{C_{eq}} = 0.227 + 0.114 = 0.341 \). Thus, \( C_{eq} = \frac{1}{0.341} \approx 2.93 \, \mu F \).

It's essential to convert microfarads to farads since farad is the standard unit of capacitance used in calculations. This means \( 2.93 \, \mu F = 2.93 \times 10^{-6} \, F \). Understanding this process is fundamental to accurately dealing with capacitors in series in any electrical circuit.

Capacitive reactance plays a crucial role in AC circuits, especially when it comes to determining how much a capacitor opposes the current flow. It is denoted by \( X_c \) and can be computed using the formula \( X_c = \frac{1}{2\pi f C} \), where \( f \) is the frequency and \( C \) is the capacitance.

In our example, with a frequency \( f = 60.0 \, Hz \) and an equivalent capacitance \( C = 2.93 \times 10^{-6} \, F \), the capacitive reactance is calculated as \( X_c = \frac{1}{2 \pi \times 60.0 \times 2.93 \times 10^{-6}} \).

After going through the calculations, we find \( X_c \approx 905 \, \Omega \). This value tells us how much the capacitors are impeding the current flow in the circuit. A higher capacitive reactance means a greater opposition to current flow, which is vital information when analyzing AC circuits.

Root Mean Square (RMS) current is a key factor in AC circuits, especially when we want to find how much current flows through the circuit for real-world AC applications. RMS values provide a meaningful representation of alternating current levels. In this context, the RMS current \( I_{rms} \) can be computed using Ohm’s Law for AC circuits.

The formula is \( I_{rms} = \frac{V_{rms}}{X_c} \), where \( V_{rms} \) is the root mean square voltage and \( X_c \) is the capacitive reactance. Given \( V_{rms} = 115 \, V \) and \( X_c = 905 \, \Omega \), the calculation is \( I_{rms} = \frac{115}{905} \approx 0.127 \, A \).

This value represents how much alternating current (AC) is effectively flowing through the circuit. Understanding RMS current is crucial for grasping the behavior of AC circuits and ensuring their efficient operation.