In alternating current, AC, theory, the voltage through an inductor leads the current by a phase angle of 90°. Complex numbers can help in this situation as when a real number is multiplied by i it rotates through 90° on the Argand diagram, with the magnitude remaining the same. This allows us to specify the impedance through an inductor as a complex number. This can be combined with a resistor to give a combined impedance of z = r + Li. If we have two such elements in a circuit, we can use complex numbers to determine the total impedance when they are in series and in parallel.In series Zt = Z1 + Z2In Parallel Add the following two impedances (a) in series and (b) in parallel.Z1 = 4 + 3i and Z2 = 12 + 5i

introduction for series for parallel

Answered: In alternating current, AC, theory, the…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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In alternating current, AC, theory, the voltage through an inductor leads the current by a phase angle of 90°. Complex numbers can help in this situation as when a real number is multiplied by i it rotates through 90° on the Argand diagram, with the magnitude remaining the same. This allows us to specify the impedance through an inductor as a complex number. This can be combined with a resistor to give a combined impedance of z = r + Li. If we have two such elements in a circuit, we can use complex numbers to determine the total impedance when they are in series and in parallel.

In series Z_t = Z₁ + Z₂

In Parallel

Add the following two impedances (a) in series and (b) in parallel.

Z₁ = 4 + 3i and Z₂ = 12 + 5i

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