# Advantages of AC over DC

- In AC system we can use transformers to change the voltage levels. It cannot be used in DC system. Electricity is generated and transmitted at high voltage due to economic reasons and utilized at low voltage due to safety reasons.
- The AC motors are cheaper, simpler in construction, efficient and require less maintenance as compared to DC motors.
- The switch gear (e.g. circuit breakers, switches etc.) for AC system is simpler than required in DC system.
- The maintenance cost of AC equipment is lesser than DC equipment.

## Generation of Alternating EMF

An alternating EMF can be generated either by rotating magnetic field within a stationary coil, or by rotating a coil within a stationary magnetic field. The EMF generated, in both cases will be a sinusoidal waveform.

The magnitude of EMF generated in coil depends upon the strength of magnetic field, the number of turns on the coil and the speed at which the coil or magnetic field rotates. The former method is employed for large sized AC generators whereas the later one is employed in small sized AC generators.

## Commonly Used Definitions in AC

**1. Wave form: **1. The wave form of an AC quantity is a graph of its magnitude against time. The wave form tells us about instantaneous changes in magnitude of an AC quantity.

**2. Cycle: **One complete set of positive and negative values of an alternating quantity is known as cycle.

**3. Amplitude or Peak value: **It is the maximum value (positive or negative) of an alternating quantity.

**4. Instantaneous value: ** It is the value of the alternating quantity at any instant.

**Equations of AC EMF**

e = E_{m}sin θ

e = E_{m}sin ωt

e = E_{m}sin (2πft)

(since ω = 2πf)

e = E_{m}sin (2πt/T) (since f = 1/T)

Where, E_{m} = Peak value of EMF.

**Equations of AC Current**

i = *I*_{m}sin θ

i = *I*_{m}sin ωt

i = *I*_{m}sin (2πft)

(since ω = 2 πf)

i = *I*_{m}sin (2πt/T) (since f = 1/T)

Where, *I*_{m} = Peak value of AC Current.

Which form of above equation is to be applied will depend

upon the data given.

**5. Time Period (T): ** It is the time required by an alternating quantity to complete one cycle.

**6. Frequency: **The number of cycles completed in one second by an alternating quantity is known as its frequency. Its unit is Hertz (Hz). The relation between time period and frequency is given by:

f = 1/T or T =1/f.

**7. Alteration: ** One half cycle is called alteration.

**8. Phase: **It is given by the amount of time (or angle) since the wave last passed through its zero value. In the figure the phase of the sine wave at point A is T/4 seconds or π/2 radian or 90^{o}.

**9. Phase Difference: **The angle difference or time difference between two sine waves since they last passed through their zero value is called phase difference. In the figure the phase difference between two sine waves is α^{o}.

**10. In-phase: ** When two sine waves achieve their maximum value or zero value at the same time, they are said to be in phase.

**11. Lag and Lead: **A sine wave which reaches its zero or maximum value later than the other is called lagging sine wave. In the figure sine wave B reaches its zero value α^{o} later than the other wave. Also, it reaches it maximum value α^{o} later. Hence, sine wave B is lagging behind sine wave A by α^{o}.

A sine wave which reaches its zero or maximum value earlier than the other is called leading sine wave. In the figure sine wave A reaches its zero value α^{o} earlier than the other wave. Also, it reaches it maximum value α^{o} earlier. Hence, sine wave A is leading the sine wave B by α^{o}.

# Form Factor

The form factor is defined as the ratio of RMS value to the average value of an alternating quantity.

Form factor (K_{f}) = RMS value / Average value

For a sinusoidal wave, form factor (K_{f}) = 0.707Im / 0.637*I*_{m} = 1.1

With the help of form factor, we can find the RMS value from the average value and vice-versa. Form factor shows the peakiness of the waveform.

A triangular wave which is peakier than a sine wave has the form factor of 1.15. On the other hand, a square wave, which is flatter than a sine wave, has a **form factor** of 1.

## Peak factor or Crest factor or Amplitude factor

The peak factor is defined as the ratio of the peak value to the RMS value of an alternating quantity.

Peak factor (K_{f}) = Peak value / RMS value

For a sinusoidal wave, peak factor (K_{f}) = 1.414

The peak factor has very importance in dielectric insulation testing. It is so because the dielectric stress on the insulation material depends on the peak value of applied voltage. The peak factor is also important when measuring iron loss because iron loss depends on the value of maximum flux.

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