This document defines and provides expressions for the root mean square (RMS) value, average value, peak factor, and form factor of an alternating current (AC). It states that the RMS value of an AC current is defined as the steady current that would produce the same heat over time and is equal to the square root of half the mean of the squared current. The average value of an AC current is defined as the area under the current waveform over one half cycle divided by the time period and is equal to 2/π times the peak current. The peak factor is the ratio of the peak current to the RMS current and equals √2. The form factor is the ratio of the RMS value to the average value and equals 1

1. Amiraj College Of
Engineering & Technology

2.  R.M.S VALUE :-
Defination
expression
R.M.S. Value of A Half HALF
Wave Rectified A.C.
 AVERAGE VALUE:-
defination
Expression
HALF Wave Rectified A.C.
 Form Factor
 Peak Factor

3.  The full form of r.m.s value is root mean square
value.
 It is given by that value of ac current and dc
current passed through circuit for same time
produced same heat energy.
 It is also define as effective or virtual value

4.  There are 2 types methods for finding r.m.s value
1)mid ordinate method
2)analytical method

5. i=𝐼 𝑚 sin 𝜔𝑡
Suppose, 𝜔𝑡= Ө
So, i=𝐼 𝑚 sin Ө
Now,
(mean of 𝑖2) = 0
2𝜋
𝑖2 𝑑𝜃
2𝜋
= 0
2𝜋
(𝐼 𝑚sin Ө)2 𝑑𝜃
=
𝐼 𝑚
2
2𝜋 0
2𝜋
sin2 𝜃𝑑𝜃
=
𝐼 𝑚
2
2𝜋 0
2𝜋 1−cos 2𝜃
2
𝑑𝜃

6. =
𝐼 𝑚
2
4𝜋
0
2𝜋
1 − cos 2𝜃 𝑑𝜃
=
𝐼 𝑚
2
4𝜋
𝜃 − sin Ө 2𝜋
0
=
𝐼 𝑚
2
4𝜋
2𝜋 − 0
(mean of 𝑖2) =
𝐼 𝑚
2
2
The r.m.s value of ac current= mean of 𝑖2
=
𝐼 𝑚
2
2
=
𝐼 𝑚
2
=0.707𝐼 𝑚

8.  It is given by that value of steady current which
transfer across the circuit and the same charge
transferred by ac quantity across the circuit in
same time.

9. i=𝐼 𝑚 sin Ө
Area of half cycle is 0
𝜋
i𝑑𝜃
Average value of ac
current=
𝑎𝑟𝑒𝑎
𝑏𝑎𝑠𝑒
= 0
𝜋
i 𝑑𝜃
𝜋
= 0
𝜋
(𝐼 𝑚 sin Ө )𝑑𝜃
𝜋
=
𝐼 𝑚
𝜋 0
𝜋
sin Ө 𝑑𝜃

10. =
𝐼 𝑚
𝜋
− cos Ө 𝜋
0
=
𝐼 𝑚
𝜋
− cos 𝜋 − cos 0
=
𝐼 𝑚
𝜋
1 − (−1 )
=
2𝐼 𝑚
𝜋
=0.637𝐼 𝑚

11. • Peak factor is defined as the ratio of
the max value to the R.M.S. value of an
alternating quantity.
• It is denoted by 𝑘 𝑎.
𝑘 𝑎 =
max value
R.M.S. value
=
𝐼 𝑚
𝐼 𝑚
2
= 1.414
• Peak factor is also called the crest
factor or the amplitude factor.

12.  Form factor is defined as the ratio of the
R.M.S. value to the average value of an
alternating quantity. It is denoted by 𝑘 𝑓.
 It is denoted by 𝑘 𝑓.
𝑘 𝑓
=
R.M.S. value
average value
𝑘 𝑓=
0.707𝐼 𝑚
0.673𝐼 𝑚
=1.11