## Info Figure 3

### Figure 2

convert 120 vac into other (usually DC) voltages, Switching power supplies are used in most compact fluorescent lights, computer power supplies, and some battery chargers. These loads behave like capacitors and are know as capacitive loads. While not as common as inductive loads, the average household uses many of these capacitive loads.

Changing alternating current electricity into an electrostatic field changes the phase relationship between the voltage and current waveforms. The situation is similar to inductive loads, only the effect is the exact opposite. The voltage waveform seems to lag behind the current waveform. Figure 3 shows shows the operation of a 1000 Watt capacitive load. Note that the voltage waveform is now lagging behind the current waveform.

The effect of either an inductive or a capacitive loads is to make the voltage and current waveforms go out of phase with each other. This effect is called reactance. As we will see when we shortly discuss power in alternating current circuits, reactance is a form of resistance that is particular to alternating current devices which are not purely resistive (i.e. the loads are either inductive or capacitive). What I have illustrated here is really an ideal look at inductive and capacitive loads. Actually all reactive loads also have resistance and the real world situation is even more complicated than shown here.

One characteristic of both inductive and capacitive loads is that they are able to store power. The inductive load stores power in its magnetic field. The capacitive load stores power in its electrostatic field. At certain instants of time, the power stored in the reactive load may be greater the power being supplied by the

### Figure 3

alternating current electricity. At this point the load actually shoves energy back at the ac power source. Hence the idea of reactance being a form of alternating current resistance not present in direct current circuits.

### Power in Resistive Circuits

Power is calculated much the same way in resistive alternating current circuits as in direct current circuits. Power (Watts) equals volts times amperes (P=EI). The only problem is that in ac power voltage and current are constantly changing amplitude and polarity. If at any instant we multiply volts times amperes, we will get the power at that instant. If we were to do this for an entire cycle of the sine wave, then we could accurately measure the amount of energy delivered to the load by that sine wave. This process (known as arithmetic integration) is best illustrated by a graph.

In Figure 4 the heavy black curve represents the ac voltage. The gray line close to the time (horizontal) axis represents current, in this case a 1000 Watt resistive load like the one shown in Figure 1. The dashed line curve is volts (at any instant) multiplied by current (at that same instant)—in other words, power. The area between this power curve and the horizontal axis represents the energy delivered by the alternating current electric power to the load. Note that the entire power sine waveform is in phase with the voltage and current waveforms. Note that the entire power waveform is positive and above the x-axis (time). All is well, power transfer in the circuit is 100%. There are no reactive components to the load, it simply sucks up all the power that the ac waveforms can deliver. Since this is an alternating current circuit, the amount of power consumed by the load is constantly changing. For a 1000 Watt resistive load the power delivered varies from zero to a peak of 2000 Watts.

AC Power, Volts & Amperes in a 1000 Watt Resistive Load

AC Power, Volts & Amperes in a 1000 Watt Inductive Load Figure 4 Power in Reactive Circuits

Power is calculated differently in reactive circuits. Instead of just volts times amps, we need to add a factor that compensates for the fact that current is out of phase with voltage. The formula for calculating real power in a reactive circuit is: 