Question

If i₁ = 3 sin wt and i₂ = 4 coswt, then i₃ is–

• A. 5 sin (wt + 53ŗ)
• B. 5 sin (wt + 37ŗ)
• C. 5 sin (wt + 45ŗ)
• D. 5 cos (wt + 53ŗ)

Answer 1

Answer: (A)

5 sin (wt + 53ŗ)

Answer 2

From Kirchoff's current law,

i₃ = i₁ + i₂ = 3 sin wt + 4 sin (wt + 90⁰)

= $\sqrt{3^{2} + 4^{2} + 2(3)(4)\cos 90º}$ sin(wt+ f)

where tan f = $\frac{4\sin 90º}{3 + 4\cos 90º}$ = $\frac{4}{3}$

\ i₃ = 5sin(wt+53⁰)