Capacitors are not useful in DC circuits since they contain insulating gaps, which are open circuits for DC. However, for voltages that change with time, a simple series circuit with a capacitor and a resistor can output the time derivative or integral of an input signal, or can filter out low-frequency or high-frequency components of a signal. But before plunging into the world of time-varying voltage and current (i.e., alternating-current circuits), we explore the voltage-divider idea using direct current, since it gives us a simple way to understand circuits containing more than one component in series. Then we apply it to the analysis of RC circuits as filters. Note that the series RC circuit can be analyzed in two different ways:

• via the exponential charging/discharging equation, and

• as an AC voltage divider.

Both approaches are valid – in fact, they are mathematically equivalent – but the first is more useful when using capacitors as integrators or differentiators, whereas the second is more useful when analyzing low-pass and high-pass filters. The first is referred to as the time-domain approach, since it considers the voltage across the capacitor as a function of time, and the second as the frequency-domain approach, since it focuses on the filter attenuation vs. frequency.