Capacitors introduce phase delay in circuits primarily through their frequency-dependent behavior, which is best analyzed using sine waves rather than square waves. In a series circuit, currents remain in phase, complicating the measurement of phase delay between voltage and current. The phase delay, or phase lag, is defined in relation to specific frequencies, making it essential to specify the input waveform conditions. Transient analysis in SPICE is not suitable for examining frequency domain characteristics; a frequency response analysis is recommended instead. Understanding these principles is crucial for accurately measuring and interpreting phase delay in capacitor circuits.