A series RLC network has R = 2 kΩ, L = 40 mH, and C = 1 μF. Calculate the impedance at resonance and at one-fourth, one-half, twice, and four times the resonant frequency.
Find the value of the impedance at resonance and at one-fourth, one-half, twice and four times the resonant frequency.
Answer to Problem 25P
The value of the impedance at resonance
Explanation of Solution
Given data:
The value of the resistor
The value of the inductor
The value of the capacitor
Formula used:
Write the expression to calculate the resonant frequency.
Here,
Write the expression to calculate the impedance at resonance of series RLC circuit.
Here,
Write the expression to calculate the impedance of the series RLC circuit.
Calculation:
Substitute
Simplify the above equation to find
(1) Impedance at resonance:
Substitute
(2) Impedance at one-fourth of the resonant frequency:
Here, the resonant frequency
Substitute
Substitute
Simplify the above equation to find
(3) Impedance at one-half of the resonant frequency:
Here, the resonant frequency
Substitute
Substitute
Simplify the above equation to find
(4) Impedance at twice of the resonant frequency:
Here, the resonant frequency
Substitute
Substitute
Simplify the above equation to find
(5) Impedance at four times of the resonant frequency:
Here, the resonant frequency
Substitute
Substitute
Simplify the above equation to find
Conclusion:
Thus, the value of the impedance at resonance
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Chapter 14 Solutions
Fundamentals of Electric Circuits
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