Post on 11-Jul-2020
(c)
P =4
9× 25
4× 30
=250
3W
Problem 7
In all parts of the problem, the following identities will be used,
∫
2π/m
0
cos(mnx) dx = 0
∫
2π/m
0
sin(mnx) dx = 0
Here m and n are integers.
(a)
V 2
1eff =1
T
∫ T
0
v2
1(t) dt
=1
T
∫ T
0
[102 + 40 cos(20t) + 2 cos(40t)] dt
= 102
⇒ V1eff = 10.0995
(b)
V 2
2eff =1
T
∫ T
0
v2
2(t) dt
=1
T
∫ T
0
[50{1 + cos(4t)} + 12.5{1 + cos(8t)} + 50{cos(6t) + cos(2t)}] dt
= 62.5
⇒ V2eff = 7.9057
(c)
V 2
3eff =1
T
∫ T
0
v2
3(t) dt
=1
T
∫ T
0
[50{1 + cos(4t)} + 36.4277{1 + cos(8t)} + 6.2499{1 − cos(8t)} + . . .] dt
= 92.6776
⇒ V3eff = 9.6269
2