Question

The current 'i' through a wire varies with time t as shown in the figure. The effective (rms) value of the current is:

• A. 6 A
• B. $2\sqrt{3}A$
• C. $2+2\sqrt{2}A$
• D. 3A

Answer 1

The correct option is B $2\sqrt{3}A$

$i=4sin\omega t+2$

$i_{rms}=\sqrt{\frac{{\int }_0^T{i}^{2}dt}{T}}$

$=\sqrt{\frac{16{\int }_0^{T}si{n}^2\omega tdt}{T}+4\frac{16{\int }_0^{T}si{n}^2\omega tdt}{T}}$

$=\sqrt{1}2=2\sqrt{3}A$