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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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A series resonant circuit has an inductive reactance of 1000W, a capac...
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A series resonant circuit has an inductive reactance of 1000W, a capac...
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.
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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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