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 \omegat. The rms current will be :

Choose the correct answer: