### Fundamentals of Alternating Current:

The electric mains supply in our homes is a voltage that varies like a sine function with time. Such a voltage is called as an alternating voltage and current driven by it is called as an alternating current. Today, most of the electrical gadgets we use require AC voltage. This is mainly because the electricity sold by the power companies is transmitted and distributes as an alternating current.

The main reason for preferring AC voltage over DC is that can be easily converted from one voltage to other by means of transformer. Alternating current varies with time that is its magnitude is constantly changing. An alternating waveform is a graph between an alternating quantity (voltage or current) and time. There are different types of waveforms viz. sinusoidal, square, and triangular. The most popular waveforms from these are sinusoidal waveforms. So, we will focus fundamentals of AC sinusoidal waveform.

#### Instantaneous value of Alternating Current:

The magnitude of an alternating quantity at any instant is called instantaneous value. It is denoted by “v” and “i” for voltage and current respectively.

#### Cycle of Alternating Current:

An alternating quantity (V or I) is said to have completed one complete cycle when it goes through a complete set of positive and negative values.

#### Alteration of Alternating Current:

One half cycle of a complete set of positive or negative values (magnitudes) is called an alteration.

#### Time period of Alternating Current:

The time taken in seconds by an alternating quantity to complete one cycle is called as time period. It is denoted by ‘T’.

#### Frequency of Alternating Current:

The number of cycles made per second by an alternating quantity is called as frequency. It is represented by ‘f’ and measured in hertz that is cycles per second.

Relation between T and f:

T=1/f or f=1/T

#### Angular velocity of Alternating Current:

It is defined as the rate of change of angular displacement. Its unit is radians per second.

It is denoted by ‘ῳ’.

ῳ= θ/T

ῳ=2πf

#### Forms of alternating voltage equations:

e= Em sinθ

e= Em sinῳt

e=Em sin2πft

e=Em sin2π/T t

#### Peak value of Alternating Current:

In above equations ‘Em’ stands for peak value. It is defined as the maximum positive or negative value which an alternating quantity attains during one complete cycle.

#### Average value of Alternating Current:

The arithmetical average of all the values of an alternating quantity over one cycle is called as an average value. The average value of alternating voltage is given by, Eavg=(e1+e2+⋯+em)/m

Eavg=1/(t2-t1) ∫_t1^t2▒〖e(t) dt〗

Average value of sinusoidal waveform:

We know that, e=Emsin θ , 0< θ<2π

Eavg=1/π ∫_0^π▒〖Em sin θ dθ〗

= Em/π ∫_0^π▒〖 sin θ dθ〗

=Em/π [-cosθ]

= Em/π [1+1]

= 2Em/π

= 0.637 Em

Eavg= 0.637 Em

#### Root mean square value of Alternating Current:

It is also called as effective value. It is defined as that steady current which when flowing through a given resistance for a given time period produces the same amount of heat as produced by the alternating current when flowing through the same resistance for the same time. In everyday use, AC voltages are always given as RMS values because this allows a sensible comparison to be made with DC voltage. For example, in India we get 230 v AC. This means 230 V AC RMS so the peak voltage is about 325.26 V!

RMS value of sinusoidal waveform:

Erms = Em/√2 = 0.707Em

#### Form factor of Alternating Current:

The ratio of effective value to the average of an alternating quantity ( V or I) is called form factor and calculated by following equation,

Form factor = (RMS value)/(Average value) = Em/√2 ÷ 2Em/π = = Em/√2 * π/2Em = 1.11

#### Peak factor of Alternating Current:

The ratio of maximum value to effective value of an alternating quantity is called peak factor.

The peak factor for alternating quantity varying sinusoidally is given by,

Peak factor= (maximum value)/(RMS value) = 1/(0.707) =1.41

#### Square wave Alternating Current:

RMS value= Em

Average value= Em

Form factor=1

Peak factor= 1

#### Triangular wave Alternating Current:

RMS value= 0.578Em

Average value= 0.5Em

Form factor= (0.578)/(0.5)=1.16

Peak factor= 1/(0.578) = 1.73

#### Phase of Alternating Current:

The fractional part of a period or cycle through which the quantity has passed from selected origin is called as the phase. For e.g. If O is the origin selected then the phase of max. value at A is T/4 or π/2 radians.

#### Phase difference of Alternating Current:

When two or more alternating quantities of the same frequency are considered simultaneously they may not pass through a particular point at the same instant in their respective cycles. In such cases two quantities have phase difference. For e.g. as shown in figure when current i1 is zero at point O, current i2 attains zero at a point which is α degrees apart. In this case i1 leads i2 by α or the phase difference between i1 and i2 is α.

#### Power of Alternating Current:

It is the rate of energy conversion. The power consumed in a circuit is never negative. In AC circuits, there are 3 types of powers viz.

*Apparent power: it is the product of RMS values of voltage and current.

Apparent power= Erms * Irms = EI

It is expressed in volt-ampere (VA) or kilo volt ampere (KVA) or mega volt ampere (MVA). It is called apparent power because it appears that product of voltage and current is power.

*Real power: In AC circuits, reactance (inductive or capacitive) is invariably present resulting in phase difference between voltage and current. Under these circumstances, voltage may be having a high value when current is near zero or vice versa. Hence, real power is less than apparent power.

Real power= apparent power * cosΦ = EIcosΦ

Where Φ is the angle between voltage and current.

*Reactive power: the power taken by pure reactance (inductive or capacitive) in a circuit is termed as reactive power. It is expressed as volt ampere reactive(VAR).

Reactive power= apparent power * sinΦ = EIsinΦ

#### Power factor of Alternating Current:

Power factor can be defined as

Cosine of angle between voltage and current.

Ratio of resistance to impedance.

Ratio of real power to apparent power.

The value of power factor can never be more than unity.

If power factor is lagging, the current lags the voltage which is possible in case of inductive circuits.

If power factor is leading, the current leads the voltage which is possible in case of capacitive circuits.

Power factor= R/Z=cosΦ = = (real power)/(apparent power).

Article by:

Guest Blogger: Tanvi Shivgan

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