Rework Prob. 14.25 if the elements are connected in parallel.
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 37P
The value of the impedance at resonance
Explanation of Solution
Given data:
In a parallel RLC network,
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 admittance at resonance of parallel RLC circuit.
Here,
Write the expression to calculate the admittance of the parallel RLC circuit.
Write the expression that shows the general relationship between admittance and impedance.
Calculation:
Substitute
Simplify the above equation to find
(1) Impedance at resonance:
Substitute
Use equation (4) to find
Substitute
(2) Impedance at one-fourth of the resonant frequency:
Here, the resonant frequency
Substitute
Substitute
Simplify the above equation to find
Use equation (4) to find
Substitute
(3) Impedance at one-half of the resonant frequency:
Here, the resonant frequency
Substitute
Substitute
Simplify the above equation to find
Use equation (4) to find
Substitute
(4) Impedance at twice of the resonant frequency:
Here, the resonant frequency
Substitute
Substitute
Simplify the above equation to find
Use equation (4) to find
Substitute
(5) Impedance at four times of the resonant frequency:
Here, the resonant frequency
Substitute
Substitute
Simplify the above equation to find
Use equation (4) to find
Substitute
Conclusion:
Thus, the value of the impedance at resonance
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Chapter 14 Solutions
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