Question

If a direct current of value ‘a’ ampere is superimposed on an alternating current I = b sin omega*t flowing
through a wire, what is the effective (rms) value of the resulting current in the circuit?

Answer 1

Answer:

Total current,

i=a+bsin(ωt)

By definition of rms value,

i

rms

=

T

∫

0

T

i

2

dt

i

rms

=

T

∫

0

T

[a

2

+b

2

sin

2

(ωt)+2absin(ωt)] dt

i

rms

=

T

∫

0

T

[a

2

+b

2

/2(1−sin(2ωt))+2absin(ωt)] dt

Average value of sin(ωt) and sin(2ωt) is 0 over a time period.

⟹i

rms

=

a

2

+

2

b

2

A