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A series resonant circuit has an inductive reactance of 1000W, a capacitive reactance of 1000W and a resistance of 0.1W. If the resonant frequency is 10 MHz, then the bandwidth of the circuit will be
- a)1 KHz
- b)10 KHz
- c)1 MHz
- d)0.1 KHz
Correct answer is option 'A'. Can you explain this answer?
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To find the bandwidth of a series resonant circuit, we need to calculate the difference between the upper and lower frequencies at which the circuit's impedance is equal to its resistance.
Given data:
Inductive reactance (XL) = 1000 Ω
Capacitive reactance (XC) = 1000 Ω
Resistance (R) = 0.1 Ω
Resonant frequency (fr) = 10 MHz
First, we need to calculate the resonant frequency (fr) using the formula:
fr = 1 / (2π√(LC))
Where L is the inductance and C is the capacitance of the circuit. Since these values are not provided, we cannot calculate the resonant frequency directly. However, we are given that the resonant frequency is 10 MHz, so we can use this value in further calculations.
Next, we can calculate the impedance (Z) of the circuit at the resonant frequency using the formula:
Z = √((R^2) + (XL - XC)^2)
Substituting the given values:
Z = √((0.1^2) + (1000 - 1000)^2)
= √((0.01) + (0)^2)
= √(0.01)
= 0.1 Ω
The bandwidth (BW) of the circuit can be calculated using the formula:
BW = fr / Q
Where Q is the quality factor of the circuit, given by:
Q = fr / Δf
Δf is the difference between the upper and lower frequencies at which the impedance is equal to the resistance (0.1 Ω in this case).
Substituting the given values:
Q = 10 MHz / 0.1 MHz
= 100
Now we can calculate the bandwidth:
BW = (10 MHz) / (100)
= 100 kHz
Therefore, the correct answer is option A) 1 kHz.
Given data:
Inductive reactance (XL) = 1000 Ω
Capacitive reactance (XC) = 1000 Ω
Resistance (R) = 0.1 Ω
Resonant frequency (fr) = 10 MHz
First, we need to calculate the resonant frequency (fr) using the formula:
fr = 1 / (2π√(LC))
Where L is the inductance and C is the capacitance of the circuit. Since these values are not provided, we cannot calculate the resonant frequency directly. However, we are given that the resonant frequency is 10 MHz, so we can use this value in further calculations.
Next, we can calculate the impedance (Z) of the circuit at the resonant frequency using the formula:
Z = √((R^2) + (XL - XC)^2)
Substituting the given values:
Z = √((0.1^2) + (1000 - 1000)^2)
= √((0.01) + (0)^2)
= √(0.01)
= 0.1 Ω
The bandwidth (BW) of the circuit can be calculated using the formula:
BW = fr / Q
Where Q is the quality factor of the circuit, given by:
Q = fr / Δf
Δf is the difference between the upper and lower frequencies at which the impedance is equal to the resistance (0.1 Ω in this case).
Substituting the given values:
Q = 10 MHz / 0.1 MHz
= 100
Now we can calculate the bandwidth:
BW = (10 MHz) / (100)
= 100 kHz
Therefore, the correct answer is option A) 1 kHz.
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A series resonant circuit has an inductive reactance of 1000W, a capacitive reactance of 1000W and a resistance of 0.1W. If the resonant frequency is 10 MHz, then the bandwidth of the circuit will bea)1 KHzb)10 KHzc)1 MHzd)0.1 KHzCorrect answer is option 'A'. Can you explain this answer?
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