Question 132: AC fundamentals

Question

An alternating current is given by the equation i = i
1
sin $$\omega$$t + i
2
cos $$\omega$$t. The rms current will be :

Accepted Answer

$${I_0} = \sqrt {I_1^2 + I_2^2 + 2{I_1}{I_2}\cos 	heta } $$
$${I_0} = \sqrt {I_1^2 + I_2^2 + 2{I_1}{I_2}\cos 90^\circ } $$
$${I_0} = \sqrt {I_1^2 + I_2^2 + 2{I_1}{I_2}(0)}  = \sqrt {I_1^2 + I_2^2} $$
We know that,
$${I_{rms}} = {{{I_0}} \over {\sqrt 2 }}$$
So, $${I_{rms}} = {{\sqrt {I_1^2 + I_2^2} } \over {\sqrt 2 }}$$

Answer

$${1 \over {\sqrt 2 }}{\left( {i_1^2 + i_2^2} \right)^{{1 \over 2}}}$$

Answer

$${1 \over {\sqrt 2 }}({i_1} + {i_2})$$

Answer

$${1 \over {\sqrt 2 }}{({i_1} + {i_2})^2}$$

Answer

$${1 \over 2}{\left( {i_1^2 + i_2^2} \right)^{{1 \over 2}}}$$

AC fundamentals

An alternating current is given by the equation i = i 1 sin $\omegat + i 2 cos \omega$t. The rms current will be :

Choose the correct answer: