First slide

Alternating current and voltage

Question

In the given figure if i₁ = 3sin $ω$ t and i₂ = 4cos $ω$ t, then i₃ is :

Moderate

A

5 sin ( $ω$ t+ 53°)
B

5 sin ( $ω$ t+ 37°)
C

5 sin ( $ω$ t+ 45°)
D

5 cos ( $ω$ t+ 53°)

Solution

$i_{3} = i_{1} + i_{2} = 5 (\frac{3}{5} sinωt + \frac{4}{5} cosωt) = 5 (sinωt . \cos 53^{o} + cosωt . \sin 53^{o}) = 5 \sin (ωt + 53^{o})$

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