§ 14-6 Effective values and power
The effective or rms value of the function f(t) is
?? Tr m s dttfTF 0 2 )(1
? ? ?? ?
?
?
?
??????
1
0
1
0 )c o s (2
1s i nc o s
2
1)(
n
nn
n
nn tncatnbtnaatf ????
? ? ??
?
?
?
?
?
?
????
?
?
T
n
nnr m s dttncaTF 0
2
1
0 )co s (2
11 ??
???????
?
??
?
?? ??
?
2/2/2/21 222120
1
2
2
0 cccca
n
n
.222120222120 ?? ???????? IIIIa n dVVVV
?
?
?
???
1
0 )s i n (2)(
n
nn tnIIti ???
?
?
???
1
0 )s i n (2)(
n
nn tnVVt ???
If
The instantaneous power
?? ip,? ])s i n (2[
1
0 ?
?
?
??
n
nn tnVV ?? ])s i n (2[
1
0 ?
?
?
??
n
nn tnII ??
The average power
?? ?? TT Tp d tTP 00 11 ])s i n (2[
1
0 ?
?
?
??
n
nn tnVV ?? dttnII
n
nn ])s i n (2[
1
0 ?
?
?
?? ??
?
?
?
???
1
00 )co s (
n
nnnn IVIV ???
?
?
??
1
00 co s
n
nnn IVIV ?
????? 22211100 c o sc o s ?? IVIVIV )( nnn ??? ??
...c o sc o s 22211100 ???? ?? IVIVIVP )( nnn ??? ??
the angle on the equivalent impedance of
the network at the angular frequency of,??n? ?n
Vn,In ---the effective values of respective sine
function.
In the special case of a single frequency sinusoidal
voltage,V0=V2=V3=…=0
111 ?? c o sIVP
For a dc voltage V1=V2=V3=…=0 P=V 0I0=VI