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?
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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
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