
Concept explainers
(a)
To find: the
(a)

Answer to Problem 36E
Explanation of Solution
Given:
Concept used:
As opposed to constant voltage circuits, in AC circuits the impedance of an element is a measure of how much the element opposes current flow when an AC voltage is applied across it. It is basically a voltage to current ratio, expressed in the frequency domain.
Impedance is a complex number which consist of a real and an imaginary part.
Where Z is the complex impedance. The real part R represents resistance, while the imaginary X represents reactance.
Calculation:
Consider the impedance as:
In the first part of the circuit.
Reactance due to capacitance
Reactance due to inductance
In the second part of the circuit.
Resistance
Reactance due to capacitance
Reactance due to inductance
Complex number that represent impedance
Complex number that represent impedance
Hence,
(b)
To find: the total impedance in the circuit.
(b)

Answer to Problem 36E
Total impedance is
Explanation of Solution
Given:
Concept used:
As opposed to constant voltage circuits, in AC circuits the impedance of an element is a measure of how much the element opposes current flow when an AC voltage is applied across it. It is basically a voltage to current ratio, expressed in the frequency domain.
Impedance is a complex number which consist of a real and an imaginary part.
Where Z is the complex impedance. The real part R represents resistance, while the imaginary X represents reactance.
Calculation:
Total impedance
Hence, total impedance is
(c)
To find: the admittance in a circuit with an impedance
(c)

Answer to Problem 36E
Admittance is
Explanation of Solution
Given:
Concept used:
As opposed to constant voltage circuits, in AC circuits the impedance of an element is a measure of how much the element opposes current flow when an AC voltage is applied across it. It is basically a voltage to current ratio, expressed in the frequency domain.
Impedance is a complex number which consist of a real and an imaginary part.
Where Z is the complex impedance. The real part R represents resistance, while the imaginary X represents reactance.
Calculation:
Now the admittance
Rationalizing the equation:
Hence, admittance is
Chapter 9 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Additional Math Textbook Solutions
Pre-Algebra Student Edition
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Elementary Statistics (13th Edition)
Introductory Statistics
Calculus: Early Transcendentals (2nd Edition)
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