Contents

POWER. 1

POWER IN AC CIRCUITS. 1

Average, MAX and min PoweR. 1

Complex Power. 1

Power factor correction. 2

Trigonometric identites Frequently used in complex power calculations. 2

INDUCTORS. 2

TRANSFORMERS. 3

DOT convention. 3

Bridge Circuits. 4

Millman’s Theorem.. 5

 

POWER

POWER IN AC CIRCUITS

Average, MAX and min PoweR

Signal

Instantaneous Power

 

 

 

Average , Maximum and Minimum power in terms of power factor (PF)

 

 

 

Complex Power

Complex Power

1.       Apparent Power is the magnitude of the complex power.

 

2.       Average/Real Power and Reactive Power is the real part and imaginary part of the complex power respectively.

 

3.       Unit of reactive power is VARS

Reactive Power (VARS)

Average Power/Real Power

 

Complex Power

1.       Apparent Power =

 

2.       The unit of apparent power is VA

 

3.       Apparent power is the magnitude of the complex power.

1.       Complex Power

2.       Real Power

3.       Reactive Power

4.       Apparent Power

 

Power factor correction

 

 

 

 

   (Lagging power factor)

   (Leading power factor)

 

 is the impedance angle, or power factor angle

 

 

 

Trigonometric identites Frequently used in complex power calculations

 

                 

 

Average value of

Average value of

 

INDUCTORS

 

Inductance of a coil with N turns, cross section area A, length L and core permeability

Voltage induced across an inductor

 

 

Voltage induced across a coil (w.r.t flux linkage )

 

Flux linkage  and current relation

 

Energy stored in an inductor

 

Magnetic equivalent of electric current

Source of EMF is battery

Source of MMF is current coil

 

 

 

 

TRANSFORMERS

DOT convention

 

 

 

A current entering the dotted terminal of one coil produces voltage with a positive voltage reference at the dotted terminal of the second coil.

 

 

 

A current entering the dotted terminal of one coil produces voltage with a positive voltage reference at the dotted terminal of the second coil.

Voltages and currents in terms of phasors

Coefficient of mutual coupling

 

Dot convention and current / voltage polarity reference

Reflection of secondary into primary

 

 

Reflection of primary into secondary

 

Current and flux direction using right hand rule

LENZ’S LAW

 

The direction of the induced voltage( in other words the current direction)will be such that it will oppose the change in the flux

General Transformer Equation

 primary or secondary RMS Voltage

 Frequency of RMS Voltage

 turns of primary or secondary

 Peak value of flux

Impedance Matching

If the transformer is acting as an impedance matching device than

 

 

 

Bridge Circuits

 

 

 

Bridge circuit can be used to determine the value of an unknown resistance.

 

 

The bridge is balanced if  or.

 

When the bridge is balanced then

 

 

 

 

 

 

Millman’s Theorem