(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