Characteristics of a Sine Wave

Electrical sin wave form graph is a showing the variation of voltage or current. The horizontal axis shows the passing of time, progressing from left to right. The vertical axis shows the quantity measured ( voltage, ampere or Power ). There are six must important characteristics of sine wave.

RMS value 

Root mean squared ( RMS ) value is the value of the equivalent direct voltage ( DC ) which would provide the same energy to a circuit as the sine wave measured. That is, if an AC sine wave has a RMS value of 230 volts, it will provide the same energy to a circuit as a DC supply of 230 volts.

RMS value Equation 

V _{RMS =} V <sub>Peek X 0.707

Example
Peek value or Max value = 326 V

V RMS = V Peek X 0.707</sub>

 V <sub>RMS = 326 X 0.707

V RMS = 230.48 V</sub>

Average Value or mean value 
This is normally taken to mean the average value of only half a cycle of the sine wave.

Mean value Equation 

V _mean = V _Peek  X 0.637

<sub>Example
Peek value or Max value = 326 V

V mean = V Peek  X 0.637
V mean =  326 X 0.637</sub>
V _{mean = 207.66 v}


Peak to Peak value

Peak to peak (pk-pk) is the difference between the maximum positive and the maximum negative amplitudes of a waveform. 

Peek to Peek value  

V_{PP =} V _Peek + V _Peek 

_Example

_{Peek value or Max value = 326 V}

_{VPP = V Peek + V Peek} 

V_{PP = 326+ 326}

_{VPP = 652 v}

Instantaneous Value 
Instantaneous value of an alternating voltage is the value of voltage at one particular instant time. The value may be zero if the particular instant is the time in the cycle at which the polarity of the voltage is changing. It may also be the same as the peak value, if the selected instant is the time in the cycle at which the voltage stops increasing and starts decreasing. There are actually an infinite number of instantaneous values between zero and the peak value.

Instantaneous value Equation

v (t) = V_Max sin (w t )

w = 2 x p  x f  or  w = 2 x p / T

v (t) = V_Max sin (2*p*f *t )

Amplitude 

Amplitude is the difference between the maximum positive and the X axis of a waveform. It is equal to peek value.

Periodic Time

periodic time is that amount of time that elapses from the start of a occurrences until the commencement of the next identical happening.

T = 1/f 

T = Periodic time

f  = Frequency 

Frequency 

Frequency is the number of occurrences of a repeating event per unit time.

F =1/T

f  = Frequency

T = Periodic time

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Practical Resistor value calculation

Resistor is a passive electrical component that reduce flow of electrical current in an electronic or Electronics circuit. resister has a linear IV ( V=IR ) characteristic. meaning that the voltage across the resistor is directly proportional to the current through the resistor.
Resisters's 10³ Symbol

Resistor In Ohms	Unit	Symbol
1	Ohm	Ω
1,000	Kilo Ohm	KΩ
1,000,000	Mega Ohm	MΩ

Resistors practical value

Resistors only come in specified values. These values are spread across multiples of ten.

1

1.2

1.5

1.8

2.2

2.7

3.3

3.91

4.7

5.6

6.8

8.2

After that, the cycle repeats, but a power of ten higher.

Resistor Color code

Color	Significant figures	Multiplier	Tolerance
Black	–	×100	-
Brown	1	×101	±1%
Red	2	×102	±2%
Orange	3	×103	-
Yellow	4	×104	-
Green	5	×105	±0.5%
Blue	6	×106	±0.25%
Violet	7	×107	±0.1%
Gray	8	×108	±0.05%
White	9	×109	-
Gold	–	×10-1	±5%
Silver	–	×10-2	±10%
None	-	-	±20%

Example Calculation

Eg 1

Red      Red    Orange   Gold    

  2               2            000        ±5% 

  22000 Ω  ±5%    Or    22 KΩ

Eg 2
Blue      Gray   Brown    Silver
  6                8            0            ±10% 
  680 Ω  ±10% 

Power rating Of Resistor 
  power rating of a resistor is the specification given with a resistor that serves to tell the maximum amount of power that the resistor can withstand. When current passes through Resistor, it normally generates heat. there for we have to find suitable wattage resistor for the Electronics circuit.
 Let's look at examples of resistors and the power ratings we would need for them for you to get a practical idea:

Resister Value                    820 Ω
Resister between Voltage     12V

P = V² / R

P =12 x 12 / 820
p = 0.1756

1/4 watt resistor would suffice and be suitable for the circuit

The common standard power ratings of resistors are 0.25W, 0.5W, 1W, 2W, 5W, 10W and 25W. So the circuit designer must choose accordingly for the circuit.

Resistor Watt range with physical size  

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Ohm's law

Ohm's Law    
For a fixed metal conductor, the temperature and other condition remaining constant the current through it is proportional to the potential difference between conductor ends.

V/I = Constant

V= IR

V  = volt 
 I  = Current
 R = Resister of the conductor between the two pints considered

we can apply V=IR  Linear resistors only.

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