Question 494: AC fundamentals

Question

If the alternating current $$I=I_1 \cos \omega t+ I_2 \sin \omega t$$ then the rms current is given by

Accepted Answer

The equation of $$A C$$ is
$$I=I_1 \cos \omega t+I_2 \sin \omega L$$
The resultant current is given by
$$I_0=\sqrt{I_1^2+I_2^2}$$
Hence, the rms current from relation is
$$I_{\mathrm{rms}}=\frac{I_0}{\sqrt{2}}=\frac{\sqrt{I_1^2+I_2^2}}{\sqrt{2}}=\sqrt{\frac{I_1^2+I_2^2}{2}}$$

Answer

$$\frac{I_1+I_2}{\sqrt{2}}$$

Answer

$$\frac{\left|I_1+I_2\right|}{\sqrt{2}}$$

Answer

$$\sqrt{\left(\frac{I_1^2+I_2^2}{2}\right)}$$

Answer

$$\sqrt{\frac{I_1^2+I_2^2}{\sqrt{2}}}$$

AC fundamentals

If the alternating current $I=I_1 \cos \omega t+ I_2 \sin \omega t$ then the rms current is given by

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