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1/100+1/(-j100) 1 0.01+j0.01 1 0.01414 Z45° = 70.71 Z–45° = 50 – j50 N || ||

1/100+1/(-j100) 1 0.01+j0.01 1 0.01414 Z45° = 70.71 Z–45° = 50 – j50 N || ||

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Im not sure how 1/.01+j.01 = 1/.01414 angle 45.

How does 70.71 angle -45 = 50-j50?

Certainly! Here's a transcription and explanation suitable for an educational website: --- ### Impedance Calculation The equation demonstrates the step-by-step calculation of a total impedance (\(Z_t\)). 1. **Initial Expression:** \[ Z_t = \frac{1}{\frac{1}{100} + \frac{1}{(-j100)}} \] 2. **Simplification Step 1:** \[ = \frac{1}{0.01 + j0.01} \] 3. **Simplification Step 2:** \[ = \frac{1}{0.01414 \angle 45^\circ} \] 4. **Magnitude and Phase Conversion:** \[ = 70.71 \angle -45^\circ \] 5. **Rectangular Form:** \[ = 50 - j50 \, \Omega \] ### Explanation: - **Impedance (\(Z_t\))** is calculated from the given complex expressions. - The initial expression is a combination of two impedances in a parallel configuration. - The transformation involves converting the expression into a polar form to simplify calculations. - Final result is given both in polar coordinates (\(70.71 \angle -45^\circ\)) and rectangular form (\(50 - j50 \, \Omega\)). Understanding these transformations is essential for solving complex impedance problems in AC circuit analysis.
Transcribed Image Text:Certainly! Here's a transcription and explanation suitable for an educational website: --- ### Impedance Calculation The equation demonstrates the step-by-step calculation of a total impedance (\(Z_t\)). 1. **Initial Expression:** \[ Z_t = \frac{1}{\frac{1}{100} + \frac{1}{(-j100)}} \] 2. **Simplification Step 1:** \[ = \frac{1}{0.01 + j0.01} \] 3. **Simplification Step 2:** \[ = \frac{1}{0.01414 \angle 45^\circ} \] 4. **Magnitude and Phase Conversion:** \[ = 70.71 \angle -45^\circ \] 5. **Rectangular Form:** \[ = 50 - j50 \, \Omega \] ### Explanation: - **Impedance (\(Z_t\))** is calculated from the given complex expressions. - The initial expression is a combination of two impedances in a parallel configuration. - The transformation involves converting the expression into a polar form to simplify calculations. - Final result is given both in polar coordinates (\(70.71 \angle -45^\circ\)) and rectangular form (\(50 - j50 \, \Omega\)). Understanding these transformations is essential for solving complex impedance problems in AC circuit analysis.
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