## Illustration 31.4: Phase Shifts

Please wait for the animation to completely load.

Assume an ideal power supply. The graph shows the voltage **(red)** across and current **(blue)** from the power supply as a function of time **(voltage is given in volts, current is given in milliamperes, and time is given in seconds)**. Restart.

We start by reviewing the current and voltage relationship for a resistive load. As you change the frequency in the animation, what happens (if anything) to the ratio of voltage to current? Notice that the voltage and current are in phase with each other in this circuit.

Try a capacitive load. What happens to the amplitude of the current as you increase the frequency? The ratio of V/I is not called a resistance for this type of load; it is called the reactance (or impedance, but impedance includes information about the phase shift between voltage and current). This means that the reactance of a capacitive load changes with frequency. Since the current increases as the frequency increases, the reactance must decrease as the frequency increases.

Notice the phase shift between the current and the voltage. Pause the graph. Which plot (the voltage or the current) is in the "lead?" In other words, if you look at a time in which the current reaches its maximum value, has the voltage already reached its maximum value or will it reach its maximum value at a slightly later time? If the current reaches its maximum first, we describe this as the "current leading the voltage, " but if the voltage reaches its maximum first, we call it "current lagging the voltage." Which is the case with a capacitor?

Try an inductive load. What happens to the amplitude of the current as you increase the frequency? Does the current lead or lag the voltage in this case? Notice that with a capacitive load the current leads the voltage, while with an inductive load the current lags the voltage.

Because the current and voltage are out of phase when there are capacitive and inductive loads, and the reactance is a function of frequency, the mathematics to calculate the voltage and current is a bit more involved, but Kirchhoff's laws still hold at any instant in time.

Illustration authored by Anne J. Cox.

Script authored by Wolfgang Christian and Anne J. Cox.