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enter image description here In the graph below, the left vertical axis of the graph is the magnitude of voltage, the green line indicating the input voltage, blue line indicating the capacitor/inductor voltage. The right vertical axis is the phase difference of the voltages. It shows that the phase lag (in the dotted blue line) slowly increases from 0 to -90° at low frequencies. We know that the impedance of a capacitor is Z=1/(iωC), if Z changes with ω, shouldn't i be constant, hence the phase difference always be 90°? enter image description here

The opposite scenario occurred in the case of an inductor, where the phase change tends to zero when the AC frequency increases. Why is that so? Would appreciate it if provided both mathematical and logical reasoning. enter image description here

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  • $\begingroup$ What resitor was in the circuit? $\endgroup$
    – trula
    Commented Apr 24 at 13:57
  • $\begingroup$ What exactly is being plotted on the vertical axes of the graphs? $\endgroup$
    – Philip Wood
    Commented Apr 24 at 14:57
  • $\begingroup$ The resistor in the circuit is 1kΩ. The left vertical axis of the graph is the magnitude of voltage, the green line indicating the input voltage, blue line indicating the capacitor/inductor voltage. The right vertical axis is the phase difference of the voltages. I have added the circuit arrangement in the post. $\endgroup$
    – Maxine
    Commented Apr 24 at 15:18

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The capacitor possesses an impedance which decreases with increasing frequency. At zero frequency it is an open circuit and at high frequencies it is a short circuit. In combination with the resistance in the circuit, it forms an RC filter which has a break frequency where the impedance of the capacitor and the resistor are equal. below this frequency the capacitor limits current and above it the resistor limits current. The phase angle swings through 90 degrees as the circuit switches over from being controlled by the cap to being controlled by the resistor.

Same thing if we replace the cap with an inductor, which has an impedance which increases with increasing frequency. At zero frequency it is a short circuit and at high frequencies it is an open circuit. It too has a break frequency where the impedance of the inductor is equal to the resistance of the resistor. Below this frequency the resistor limits current and above it the inductor limits current. The phase angle swings through 90 degrees as the circuit switches over from being controlled by the inductor to being controlled by the resistor.

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