Q:
Currents I?, I? and I? meet at a junction in a circuit. All currents are marked as entering the node. If I? = -6sin(?t) mA and I? = 8 cos(?t) mA, the I? is ________
Answer & Explanation
Answer: D) -10 cos(?t + 36.87) mA
Explanation: Applying KCL, we get, I? + I? + I? = 0
? -6 sin(?t) + 8 cos(?t) + I? = 0
? I? = 6 sin (?t) – 8 cos (?t)
= 10[sin (?t).sin (36.86) – cos (?t) cos (36.86)]
=-10[cos (?t) cos (36.86) – sin (?t) sin (36.86)]
= -10 cos (?t + 36.86)
[As, cos (A+B) = cosA.cosB – sinA.sinB].
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