Checking Kirchhoff's current law

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SUMMARY

This discussion focuses on applying Kirchhoff's Current Law (KCL) to a serial circuit with a resistor and inductor, specifically addressing a circuit with a 2 Ω resistor in series with an inductor. The calculated current, IZ, is 330.562 mA, but the proof is deemed incorrect due to the non-purely reactive nature of the branch. Participants are asked to determine the phase angle of the impedance in this circuit configuration.

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Homework Statement
Prove the law
Relevant Equations
KCL
Im trying to apply KCL to the serial c and parallel rl circuit.
Screenshot 2020-11-04 at 22.24.09.png


IZ =
1604525094368.png
=
1604525094402.png
= 330.562 mA
but this means incorrect proof.
Anyone can help please?
 
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Note the 2 Ω resistance in series with the inductor. The branch is not purely reactive in nature. The current through that branch will not be purely 90° out of phase with the current through the resistor branch.

Can you find the phase angle of the impedance of that branch?
 

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