In the given figure, if i1=3sinω t and i2=4cosω t , then i3 is

Question

In the given figure, if i1=3sinω t and i2=4cosω t , then i3 is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-cgqwibnornvtyeu8.jpg" /> (A) 5 text sin (ω t + 53 ° ) (B) 5 text sin (ω t + 37 ° ) (C) 5 text sin (ω t + 45 ° ) (D) 5 text cos (ω t + 53 ° )

Tardigrade Admin · Accepted Answer

i3=i1+i2 ⇒ i3 = 3 sinω t + 4 cosω t ⇒ i3 = 5 ((3/5) sin ω t + (4/5) cos ω t) ⇒ i3 = 5 (cos 53 ° sin ω t + sin 53 ° cos ω t) ⇒ i3=5 text sin (ω t + 53 ° )

Q. In the given figure, if $i_{1} = 3 s inω t$ and $i_{2} = 4 cos ω t$ , then $i_{3}$ is

$5 sin (ω t + 5 3^{\circ})$

$5 sin (ω t + 3 7^{\circ})$

$5 sin (ω t + 4 5^{\circ})$

$5 cos (ω t + 5 3^{\circ})$

$i_{3} = i_{1} + i_{2}$
$\Rightarrow i_{3} = 3 s inω t + 4 cos ω t$
$\Rightarrow i_{3} = 5 (\frac{3}{5} s inω t + \frac{4}{5} cos ω t)$
$\Rightarrow i_{3} = 5 (cos 5 3^{\circ} s inω t + s in 5 3^{\circ} cos ω t)$
$\Rightarrow i_{3} = 5 sin (ω t + 5 3^{\circ})$

Q. In the given figure, if i1​=3sinωt and i2​=4cosωt , then i3​ is

5 sin (ωt+53∘)

5 sin (ωt+37∘)

5 sin (ωt+45∘)

5 cos (ωt+53∘)