Phasors Explained
Learning Goal: To understand the concept of phasor diagrams and be able to use them to analyze AC circuits (those with sinusoidally varying current and voltage).
Phasor diagrams provide a convenient graphical way of representing the quantities that change with time along with , which makes such diagrams useful for analyzing AC circuits with their inherent phase shifts between voltage and current. You have studied the behavior of an isolated resistor, inductor, and capacitor connected to an AC source. However, when a circuit contains more than one element (for instance, a resistor and a capacitor or a resistor and an inductor or all three elements), phasors become a useful tool that allows us to calculate currents and voltages rather easily and also to visualize some important processes taking place in the AC circuit, such as resonance.

Let us assume that a certain quantity changes over time as . A phasor is a vector whose length represents the amplitude (see the diagram ).This vector is assumed to rotate counterclockwise with angular frequency ; that way, the horizontal component of the vector represents the actual value at any given moment.

In this problem, you will answer some basic questions about phasors and prepare to use them in the analysis of various AC circuits.
In parts A - C consider the four phasors shown in the diagram . Assume that all four phasors have the same angular frequency .
Part A
At the moment depicted in the diagram, which of the following statements is true?
Part B
At the moment shown in the diagram, which of the following statements is true?
 lags by . lags by . lags by . lags by .
Part C
At the moment shown in the diagram, which of the following statements is true?
 leads by . lags by . leads by . lags by .
Let us now consider some basic applications of phasors to AC circuits.
• For a resistor, the current and the voltage are always in phase.
• For an inductor, the current lags the voltage by .
• For a capacitor, the current leads the voltage by .
Part D
Consider this diagram. Let us assume that it describes a series circuit containing a resistor, a capacitor, and an inductor. The current in the circuit has amplitude , as indicated in the figure.

Which of the following choices gives the correct respective labels of the voltages across the resistor, the capacitor, and the inductor?