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The rms value of current $$ i(t) =I_1 \sin \omega t + I_2 \sin 2\omega t $$ is:
$$ (I_1^2 + I_2^2)^{\frac {1}{2}} $$
$$ \left( \frac {I_1 ^2} {2} + \frac {I_2 ^2} {2}\right)^ \frac {1}{2} $$
$$ \left( \frac {I_1 ^2} {2} + {2I_2 ^2}\right)^ \frac {1}{2} $$
$$ \left( \frac {I_1 ^2} {2} + {4I_2 ^2}\right)^ \frac {1}{2} $$
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