Currents I1, I2 and I3 meet at a junction in a circuit. All currents are marked as entering the node. If I1 = -6sin(ωt) mA and I2 = 8 cos(ωt) mA, the I3 is ________(a) 10 cos(ωt + 36.87) mA(b) 14 cos(ωt + 36.87) mA(c) -14 sin(ωt + 36.87) mA(d) -10 cos(ωt + 36.87) mAI got this question in an interview for job.Query is from Advanced Problems on Network Theory topic in chapter Network Theory and Complex Circuit Diagram of Network Theory

Currents I1, I2 and I3 meet at a junction in a circuit. All currents a

1.	Currents I1, I2 and I3 meet at a junction in a circuit. All currents are marked as entering the node. If I1 = -6sin(ωt) mA and I2 = 8 cos(ωt) mA, the I3 is ________(a) 10 cos(ωt + 36.87) mA(b) 14 cos(ωt + 36.87) mA(c) -14 sin(ωt + 36.87) mA(d) -10 cos(ωt + 36.87) mAI got this question in an interview for job.Query is from Advanced Problems on Network Theory topic in chapter Network Theory and Complex Circuit Diagram of Network Theory
Answer» Correct choice is (d) -10 cos(ωt + 36.87) mA To explain I would SAY: Applying KCL, we get, I1 + I2 + I3 = 0 ∴ -6 sin(ωt) + 8 cos(ωt) + I3 = 0 ∴ I3 = 6 sin (ωt) – 8 cos (ωt) = 10[sin (ωt).sin (36.86) – cos (ωt) cos (36.86)] =-10[cos (ωt) cos (36.86) – sin (ωt) sin (36.86)] = -10 cos (ωt + 36.86) [As, cos (A+B) = cosA.cosB – sinA.sinB].

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