Question
What is the rms value of alternating current shown in figure?
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Answer
$(\text{I}^2)_{\text{mean}}=\frac{\int\limits^{\text{T}}_{0}\text{I}^2\text{dt}}{\int\text{dt}}=\frac{\int\limits^{\frac{\text{T}}{2}}_0(2)^2\text{dt}+\int\limits^{\text{T}}_{\frac{\text{T}}{2}}(-2)^2\text{dt}}{\text{T}}=\frac{\int\limits^{\text{T}}_04\text{dt}}{\text{T}}=4$
$\text{I}_{\text{rms}}=\sqrt{4}=2\text{A}$
$\text{I}_{\text{rms}}=\sqrt{4}=2\text{A}$
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