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1.2.1 Complex Power

• Consider the basic power equation,

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1.2.1.1 - Real Power

• The relationship for real power is shown below where the current and resistance are in phase (although the values are rarely perfectly in phase).

• When the current and voltage are D.C. (not charging) the circuit contains pure resistance, and the power is constantly dissipated as heat or otherwise. Notice that the value of P will always be positive, thus it never returns power to the circuit.

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1.2.1.2 - Average Power

• An average power can be a good measure of real power consumption of a resistive component.

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1.2.1.3 - Reactive Power

• When we have a circuit component that has current ±90° out of phase with the voltage it uses reactive power. In this case the net power consumption is zero, in actuality the power is stored in and released from magnetic or electric fields.

• Consider the following calculations,

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1.2.1.4 - Apparent Power

• In all circuits we have some combination of Real and Reactive power. We can combine these into one quantity called apparent power,

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1.2.1.5 - Complex Power

• We can continue the examination of power by assuming each is as below,

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1.2.1.6 - Power Factor

• The power factor (p.f.) is a good measure of how well a power source is being used.

• It is common to try to correct power factor values when in industrial settings. For example, if a large motor were connected to a power grid, it would introduce an inductive effect. Capacitors can be added to compensate.

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1.2.1.7 - Average Power Calculation

• If we want to find the average power, consider the following,

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1.2.1.8 - Maximum Power Transfer

• Consider the thevenin circuit below. We want to find the maximum power transfered from this circuit to the external resistance.