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A condenser of 250 µF is connected in parallel to a coil of inductance 0.16 mH and effective resistance 20 W. The resonant frequency will be ______ (give Answer in KHz)
Correct answer is '80º KHz'. Can you explain this answer?
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A condenser of 250 µF is connected in parallel to a coil of induc...
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Given information:
- Condenser of 250 F
- Coil of inductance 0.16 mH and effective resistance 20 W
To find:
Resonant frequency in KHz
Solution:
1. Resonant Frequency:
The resonant frequency of an RLC circuit can be calculated using the formula:
f_res = 1 / (2π√(LC))
Where:
f_res = Resonant frequency
L = Inductance
C = Capacitance
2. Capacitive Reactance:
The capacitive reactance (Xc) of the condenser can be calculated using the formula:
Xc = 1 / (2πfC)
Where:
Xc = Capacitive reactance
f = Frequency
C = Capacitance
3. Inductive Reactance:
The inductive reactance (Xl) of the coil can be calculated using the formula:
Xl = 2πfL
Where:
Xl = Inductive reactance
f = Frequency
L = Inductance
4. Impedance:
The impedance (Z) of the RLC circuit can be calculated using the formula:
Z = √(R^2 + (Xl - Xc)^2)
Where:
Z = Impedance
R = Resistance
Xl = Inductive reactance
Xc = Capacitive reactance
5. Resonance condition:
At resonance, the capacitive and inductive reactances are equal, i.e., Xl = Xc.
6. Calculation:
Using the given values, we can calculate the resonant frequency as follows:
Xc = 1 / (2πfC)
Xl = 2πfL
At resonance, Xl = Xc, so we can equate the above two equations:
2πfL = 1 / (2πfC)
Simplifying the equation further:
f^2 = 1 / (4π^2LC)
Taking the square root of both sides:
f = 1 / (2π√(LC))
Substituting the given values:
f = 1 / (2π√(0.16 mH * 250 F))
f ≈ 1 / (2π√(0.16 * 0.00025))
f ≈ 1 / (2π√(0.00004))
f ≈ 1 / (2π * 0.00632)
f ≈ 1 / (0.0398)
f ≈ 25.13 Hz
Converting the frequency to KHz:
f ≈ 25.13 * 10^-3 KHz
f ≈ 0.02513 KHz
Therefore, the resonant frequency is approximately 0.02513 KHz or 25.13 Hz.
- Condenser of 250 F
- Coil of inductance 0.16 mH and effective resistance 20 W
To find:
Resonant frequency in KHz
Solution:
1. Resonant Frequency:
The resonant frequency of an RLC circuit can be calculated using the formula:
f_res = 1 / (2π√(LC))
Where:
f_res = Resonant frequency
L = Inductance
C = Capacitance
2. Capacitive Reactance:
The capacitive reactance (Xc) of the condenser can be calculated using the formula:
Xc = 1 / (2πfC)
Where:
Xc = Capacitive reactance
f = Frequency
C = Capacitance
3. Inductive Reactance:
The inductive reactance (Xl) of the coil can be calculated using the formula:
Xl = 2πfL
Where:
Xl = Inductive reactance
f = Frequency
L = Inductance
4. Impedance:
The impedance (Z) of the RLC circuit can be calculated using the formula:
Z = √(R^2 + (Xl - Xc)^2)
Where:
Z = Impedance
R = Resistance
Xl = Inductive reactance
Xc = Capacitive reactance
5. Resonance condition:
At resonance, the capacitive and inductive reactances are equal, i.e., Xl = Xc.
6. Calculation:
Using the given values, we can calculate the resonant frequency as follows:
Xc = 1 / (2πfC)
Xl = 2πfL
At resonance, Xl = Xc, so we can equate the above two equations:
2πfL = 1 / (2πfC)
Simplifying the equation further:
f^2 = 1 / (4π^2LC)
Taking the square root of both sides:
f = 1 / (2π√(LC))
Substituting the given values:
f = 1 / (2π√(0.16 mH * 250 F))
f ≈ 1 / (2π√(0.16 * 0.00025))
f ≈ 1 / (2π√(0.00004))
f ≈ 1 / (2π * 0.00632)
f ≈ 1 / (0.0398)
f ≈ 25.13 Hz
Converting the frequency to KHz:
f ≈ 25.13 * 10^-3 KHz
f ≈ 0.02513 KHz
Therefore, the resonant frequency is approximately 0.02513 KHz or 25.13 Hz.
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A condenser of 250 µF is connected in parallel to a coil of inductance 0.16 mH and effective resistance 20 W. The resonant frequency will be ______ (give Answer in KHz)Correct answer is '80º KHz'. Can you explain this answer?
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