#### Power in Resistive AC Circuits:

When ac source is connected with circuit and circuit is resistive then voltage and current are in-phase. In-phase means that two waveforms arrive at their peak positive values,zero values and peak negative values simultaneously with alternating current values of voltage and current varies with time and at any instant power is equal to the current at that instant multiplied by voltage at that instant. Never forget that power wavefrom is always positive for in-phase current and voltage.  #### Power in Out-of-Phase Circuits:

All circuits are not only composed of resistance.

#### Reactance:

The oppositon given to current by capacitors and inductors in case of ac circuit. Both resistance and reactance sounds same but they are totally different. It causes 90 degree out of phase with one another.

#### Capacitive Reactance:

The reactance of a capacitor called reactive capacitance cause the current to lead the voltage. In capacitive reactance when voltage is zero current already reaches it’s maximum value. Thus the current leads voltage by 90 degree.

#### Inductive Reactance:

The reactance of a inductor is called inductive reactance cause the current to lag the voltage. In inductive reactance current lags 90 degree when voltage is reference line (zero). Since a capacitive and inductive reactances cause a 90 degree phase shift, from this thing we can conclude that only resistance uses power. The figure given above conclude different things. #### Phase Shift:

Circuits in which phase-shift occurs are not easy to find there power by multiplying current and voltage. In circuits with combination load conclude several things.

1. The resistive part of the circuit use power. In the resistance part current and voltage are in phase.

2. The reactance part of the circuit uses no power the current and voltage are 90 degree out of phase.

3. The phase relationship between the total voltage and the current is determined by the relative amount of resistance and reactance. #### Phasors:

It is a graphical representation of electrical quantities in terms of angle. Direction represents the phase angle in electrical degrees whose length represents the magnitude of electrical quantity.  The figure given above is a phasor diagram of current 10A at 60 degree.  in this figure current and voltage relationship represents in terms of phasors showing that current is 5A and voltage is 10V and current leads the voltage by 45 degree.

Functions of Right Triangle:

Trigonometric functions are very important in mathematics and engineering they have a lot of applications.

From earlier classes we studying about trigonometric functions specially (sin , cos , tan)  True Power:

is the actual power consumed by equipment to do usual work. We can also determine it with wattmeter.

Reactive Power:

exist in ac circuit when the current and voltage are not in phase. It is expressed as (var).

Apparent Power:

It is combination of reactive and true power. It is expressed as (VA). It is product of rms current and rms voltage.

#### Power Factor (PF):

The ratio of true power to the apparent power in a circuit is known as power factor. It is represents in terms of Cos

PF = cos = P / P app

when current and voltage are in phase there power factor is 1, the true power is same as apparent power. When current and voltage are 90 degree out of phase, the power factor is 0.

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