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Calculate the impedance Zab of the following combinations shown below. 50 2 а) a W-b 502 1uF b) frequency = 1 kHz a MHE b 202 60uF c) frequency = 20 kHz a WHE b 502 a b d) frequency = 500 Hz 10mH 4kN 40pF e) frequency =1 MHz a 1mH

Calculate the impedance Zab of the following combinations shown below. 50 2 а) a W-b 502 1uF b) frequency = 1 kHz a MHE b 202 60uF c) frequency = 20 kHz a WHE b 502 a b d) frequency = 500 Hz 10mH 4kN 40pF e) frequency =1 MHz a 1mH

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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Please answer all parts. Attached is the formula sheet that you need to use. Please answer all parts
## Formulas: - \( \omega = 2 \times \pi \times f \) - \( A \cos(\omega t + \theta) \rightarrow A \angle \theta \) - \( V = I \ast Z \) ### Polar to Rectangular: - **Polar:** \( R \angle \theta \) - \( a = R \times \sin \theta \) - \( b = R \times \cos \theta \) **Rectangular:** \( a + jb \) ### Rectangular to Polar: - **Rectangular:** \( a + jb \) - \( R = \sqrt{a^2 + b^2} \) - \( \theta = \tan^{-1} \frac{b}{a} \) **Polar:** \( R \angle \theta \) --- ### Component Values and Impedance Table: | Component | Value | Reactance (X) | Impedance Z (Rectangular) | Impedance Z (Polar) | |-----------|--------|---------------------|---------------------------|----------------------| | Resistor | \( R \) | \( R \) | \( R + 0j \) | \( R \angle 0 \) | | Capacitor | \( C \) | \( \frac{1}{\omega C} \) or \( \frac{1}{2 \pi f C} \) | \( \frac{1}{j \omega C} \) or \(-j \frac{1}{\omega C} \) | \( \frac{1}{\omega C} \angle -90^\circ \) | | Inductor | \( L \) | \( \omega L \) or \( 2 \pi f L \) | \( j \omega L \) | \( \omega L \angle 90^\circ \) | - **Admittance \( Y \) = \(\frac{1}{\text{Impedance } Z}\)** --- ### Impedance Phasors: - Always draw impedance phasors with reference to resistor impedance. For example, with a 200-ohm resistor, an inductor with impedance of 100 ohms, and a capacitor with impedance of 1000 ohms: - **Phasor Diagram:** - 100∠90° -
Transcribed Image Text:## Formulas: - \( \omega = 2 \times \pi \times f \) - \( A \cos(\omega t + \theta) \rightarrow A \angle \theta \) - \( V = I \ast Z \) ### Polar to Rectangular: - **Polar:** \( R \angle \theta \) - \( a = R \times \sin \theta \) - \( b = R \times \cos \theta \) **Rectangular:** \( a + jb \) ### Rectangular to Polar: - **Rectangular:** \( a + jb \) - \( R = \sqrt{a^2 + b^2} \) - \( \theta = \tan^{-1} \frac{b}{a} \) **Polar:** \( R \angle \theta \) --- ### Component Values and Impedance Table: | Component | Value | Reactance (X) | Impedance Z (Rectangular) | Impedance Z (Polar) | |-----------|--------|---------------------|---------------------------|----------------------| | Resistor | \( R \) | \( R \) | \( R + 0j \) | \( R \angle 0 \) | | Capacitor | \( C \) | \( \frac{1}{\omega C} \) or \( \frac{1}{2 \pi f C} \) | \( \frac{1}{j \omega C} \) or \(-j \frac{1}{\omega C} \) | \( \frac{1}{\omega C} \angle -90^\circ \) | | Inductor | \( L \) | \( \omega L \) or \( 2 \pi f L \) | \( j \omega L \) | \( \omega L \angle 90^\circ \) | - **Admittance \( Y \) = \(\frac{1}{\text{Impedance } Z}\)** --- ### Impedance Phasors: - Always draw impedance phasors with reference to resistor impedance. For example, with a 200-ohm resistor, an inductor with impedance of 100 ohms, and a capacitor with impedance of 1000 ohms: - **Phasor Diagram:** - 100∠90° -
### Transcription for Educational Website #### Calculate the Impedance \( Z_{ab} \) of the Following Combinations: Below are several circuits for which you need to calculate the impedance \( Z_{ab} \). Each circuit consists of a combination of resistors, capacitors, and inductors. --- ### a) - **Components:** - A resistor of \( 50 \, \Omega \) - Terminals \( a \) and \( b \) are attached at either end of the resistor. --- ### b) - **Components:** - A resistor of \( 50 \, \Omega \) in series with a capacitor of \( 1 \, \mu F \). - Frequency: \( 1 \, \text{kHz} \) - Terminals \( a \) and \( b \) are at either end of the series combination. --- ### c) - **Components:** - A resistor of \( 20 \, \Omega \) in series with a capacitor of \( 60 \, \mu F \). - Frequency: \( 20 \, \text{kHz} \) - Terminals \( a \) and \( b \) are at either end of the series combination. --- ### d) - **Components:** - A resistor of \( 50 \, \Omega \) in parallel with an inductor of \( 10 \, \text{mH} \). - Frequency: \( 500 \, \text{Hz} \) - Terminals \( a \) and \( b \) connect this parallel combination. --- ### e) - **Components:** - A resistor of \( 4 \, \text{k} \Omega \) in series with a capacitor of \( 40 \, \text{pF} \), and both in parallel with an inductor of \( 1 \, \text{mH} \). - Frequency: \( 1 \, \text{MHz} \) - Terminals \( a \) and \( b \) encompass this entire combination. --- Please calculate the impedance for each combination using the provided frequency values.
Transcribed Image Text:### Transcription for Educational Website #### Calculate the Impedance \( Z_{ab} \) of the Following Combinations: Below are several circuits for which you need to calculate the impedance \( Z_{ab} \). Each circuit consists of a combination of resistors, capacitors, and inductors. --- ### a) - **Components:** - A resistor of \( 50 \, \Omega \) - Terminals \( a \) and \( b \) are attached at either end of the resistor. --- ### b) - **Components:** - A resistor of \( 50 \, \Omega \) in series with a capacitor of \( 1 \, \mu F \). - Frequency: \( 1 \, \text{kHz} \) - Terminals \( a \) and \( b \) are at either end of the series combination. --- ### c) - **Components:** - A resistor of \( 20 \, \Omega \) in series with a capacitor of \( 60 \, \mu F \). - Frequency: \( 20 \, \text{kHz} \) - Terminals \( a \) and \( b \) are at either end of the series combination. --- ### d) - **Components:** - A resistor of \( 50 \, \Omega \) in parallel with an inductor of \( 10 \, \text{mH} \). - Frequency: \( 500 \, \text{Hz} \) - Terminals \( a \) and \( b \) connect this parallel combination. --- ### e) - **Components:** - A resistor of \( 4 \, \text{k} \Omega \) in series with a capacitor of \( 40 \, \text{pF} \), and both in parallel with an inductor of \( 1 \, \text{mH} \). - Frequency: \( 1 \, \text{MHz} \) - Terminals \( a \) and \( b \) encompass this entire combination. --- Please calculate the impedance for each combination using the provided frequency values.
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