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# If $i= 3 \sin tw$ and $i_2= 4 \cos wt$ find $i_3$

$(a)\;5 \sin (wt+\tan^{-1} 3/4) \\ (b)\;5 \sin (wt+\tan^{-1} 4/3) \\ (c)\;5 \sin (\tan^{-1} 3/4) \\ (d)\;5 \sin wt$

Can you answer this question?

From Kiochoff's law,
$i_3 =i_1+i_2$
$\quad= 3 \sin wt+ 4 \cos wt$
$\quad= 5 \bigg(\large\frac{3}{5}$$\sin wt +\large\frac{4}{5}$$ \cos wt \bigg)$
$\quad= 5 \sin (wt+\tan^{-1} 4/3)$
Hence b is the correct answer.
answered Feb 13, 2014 by