For the circuit in Fig. 14.83, find:
- (a) the resonant frequency ω0
- (b) Zin(ω0)
Figure 14.83
a.
Find the value of the resonant frequency
Answer to Problem 44P
The value of the resonant frequency
Explanation of Solution
Given data:
Refer to Figure 14.83 in the textbook.
Formula used:
Write a general expression to calculate the impedance of a resistor in frequency domain.
Here,
Write a general expression to calculate the impedance of an inductor in frequency domain.
Here,
Write a general expression to calculate the impedance of a capacitor in frequency domain.
Here,
Calculation:
The given circuit is redrawn as Figure 1.
The Figure 1 is converted into frequency domain and drawn as Figure 2 using the equations (1), (2), and (3).
Refer to Figure 2, the resistor
Write the expression to calculate impedance of the circuit in Figure 2.
Simplify the above equation to find
Multiply and divide the above equation by the conjugate of denominator to find
Simplify the above equation to find
Equate the imaginary part to zero in equation (4).
Simplify the above equation.
Rearrange the above equation to find
Take square root on both sides of the above equation to find
Substitute
Simplify the above equation to find
Conclusion:
Thus, the value of the resonant frequency
b.
Find the value of the input impedance
Answer to Problem 44P
The value of the input impedance
Explanation of Solution
Calculation:
From part a,
To find
Substitute
To find
Substitute
Substitute
Conclusion:
Thus, the value of the input impedance
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Chapter 14 Solutions
Fundamentals Of Electric Circuits + 1 Semester Connect Access Card
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