Question 128: AC fundamentals

Question

An AC current is given by I = I
1
sin$$\omega$$t + I
2
cos$$\omega$$t. A hot wire ammeter will give a reading :

Accepted Answer

$${I_{RMS}} = \sqrt {{{\int {{I^2}dt} } \over {\int {dt} }}} $$
$$I_{RMS}^2 = \int\limits_0^T {{{{{({I_1}\sin \omega t + {I_2}\cos \omega t)}^2}dt} \over T}} $$
$$ = {1 \over T}\int\limits_0^T {(I_1^2{{\sin }^2}\omega t + I_2^2{{\cos }^2}\omega t + 2{I_1}{I_2}\sin \omega t\cos \omega t)dt} $$
$$ = {{I_1^2} \over 2} + {{I_2^2} \over 2} + 0$$
$${I_{RMS}} = \sqrt {{{I_1^2 + I_2^2} \over 2}} $$

Answer

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

Answer

$$\sqrt {{{I_1^2 - I_2^2} \over 2}} $$

Answer

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

Answer

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

AC fundamentals

An AC current is given by I = I 1 sin$\omegat + I 2 cos\omega$t. A hot wire ammeter will give a reading :

Choose the correct answer: