f the calculation for a current in a circuit were given below, find the time domain expression for the current assuming the circuit were operating at a frequency of 1000 Hz. 6- j12 + 5230° A 4 + j4
f the calculation for a current in a circuit were given below, find the time domain expression for the current assuming the circuit were operating at a frequency of 1000 Hz. 6- j12 + 5230° A 4 + j4
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![**Complex Current Calculation in an AC Circuit**
In this example, we are tasked with finding the time domain expression for the current in a circuit operating at a frequency of 1000 Hz.
Given the complex current:
\[
I = \frac{6 - j12}{4 + j4} + 5 \angle 30^\circ \, \text{A}
\]
To solve this problem, the following steps are typically involved:
1. **Simplify the Complex Fraction:** Calculate the division of complex numbers \((6 - j12)/(4 + j4)\) using complex arithmetic.
2. **Convert Polar Form to Time Domain:** Transform the polar form \(5 \angle 30^\circ\) into a sinusoidal function for the time domain using the frequency given.
3. **Combine Results:** Add the results from the complex fraction and the polar form conversion for the complete time domain solution.
This comprehensive approach allows one to express the current as a function of time, reflecting both magnitude and phase changes in an AC circuit. Understanding these calculations is crucial for analyzing and designing electrical circuits.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11b54239-8e64-41df-bbac-e376c02f6bfa%2F6abf9eba-b825-4935-9404-90d4d72e66c4%2Foafosa_processed.png&w=3840&q=75)
Transcribed Image Text:**Complex Current Calculation in an AC Circuit**
In this example, we are tasked with finding the time domain expression for the current in a circuit operating at a frequency of 1000 Hz.
Given the complex current:
\[
I = \frac{6 - j12}{4 + j4} + 5 \angle 30^\circ \, \text{A}
\]
To solve this problem, the following steps are typically involved:
1. **Simplify the Complex Fraction:** Calculate the division of complex numbers \((6 - j12)/(4 + j4)\) using complex arithmetic.
2. **Convert Polar Form to Time Domain:** Transform the polar form \(5 \angle 30^\circ\) into a sinusoidal function for the time domain using the frequency given.
3. **Combine Results:** Add the results from the complex fraction and the polar form conversion for the complete time domain solution.
This comprehensive approach allows one to express the current as a function of time, reflecting both magnitude and phase changes in an AC circuit. Understanding these calculations is crucial for analyzing and designing electrical circuits.
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