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A parallel RLC circuit resonates at 100 kHz. At frequency of 110khz. The circuit impedance will be?
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A parallel RLC circuit resonates at 100 kHz. At frequency of 110khz. T...
Parallel RLC Circuit Impedance Calculation
Given Information:
- Resonant frequency, fr = 100 kHz
- Operating frequency, f = 110 kHz
Determination of Impedance:
The impedance of a parallel RLC circuit can be calculated using the following formula:
Z = R || [(1/jωC) - jωL]
Where,
- Z = Impedance in ohms
- R = Resistance in ohms
- C = Capacitance in farads
- L = Inductance in henries
- ω = Angular frequency in radians/second
Calculation:
Given that the circuit resonates at 100 kHz, the resonant angular frequency can be calculated as follows:
ωr = 2πfr = 2 × 3.14 × 100 × 103 = 628,318.53 rad/s
At resonance, the impedance of the circuit is purely resistive and is given by:
Zr = R
Let's assume that the resistance of the circuit is R = 100 Ω. Now, we can calculate the capacitance and inductance of the circuit using the resonant frequency as follows:
ωr = (1 / √LC)
L = 1 / (Cωr2)
C = 1 / (Lωr2)
Substituting the values, we get:
L = 5.08 mH, C = 31.84 nF
Now, we can calculate the impedance of the circuit at the operating frequency of 110 kHz using the same formula:
ω = 2πf = 2 × 3.14 × 110 × 103 = 689,405.49 rad/s
Z = R || [(1/jωC) - jωL]
Z = 100 || [(1/j(689,405.49)(31.84 × 10-9)) - j(689,405.49)(5.08 × 10-3)]
Z = 100 || (0.000013 - 3.51j)
Z = 100 || 3.51∠-89.19°
Z = 3.52 - j99.98 Ω
Conclusion:
Therefore, the impedance of the parallel RLC circuit at an operating frequency of 110 kHz is 3.52 - j99.98 Ω.
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A parallel RLC circuit resonates at 100 kHz. At frequency of 110khz. The circuit impedance will be?
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A parallel RLC circuit resonates at 100 kHz. At frequency of 110khz. The circuit impedance will be? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A parallel RLC circuit resonates at 100 kHz. At frequency of 110khz. The circuit impedance will be? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parallel RLC circuit resonates at 100 kHz. At frequency of 110khz. The circuit impedance will be?.
A parallel RLC circuit resonates at 100 kHz. At frequency of 110khz. The circuit impedance will be? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A parallel RLC circuit resonates at 100 kHz. At frequency of 110khz. The circuit impedance will be? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parallel RLC circuit resonates at 100 kHz. At frequency of 110khz. The circuit impedance will be?.
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