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Calculate the value of the feedback resistor if the voltage gain Av of 12 and an input resistor of 1.3kΩ was read from the non-inverting operational amplifier.

Computer Science

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Answer

14.3 kΩ\text{14.3 k}\Omega

Step-by-step solution

4 steps
  1. Identify the given values and the formula for a non-inverting operational amplifier.

    The voltage gain (AvA_v) for a non-inverting operational amplifier is given by the formula:

    Av=1+RfR1A_v = 1 + \frac{R_f}{R_1}

    Given values:

    • Voltage gain, Av=12A_v = 12
    • Input resistor, R1=1.3 kΩ=1300 ΩR_1 = 1.3 \, \text{k}\Omega = 1300 \, \Omega
  2. Substitute the given values into the formula.

    12=1+Rf1300 Ω12 = 1 + \frac{R_f}{1300 \, \Omega}
  3. Rearrange the equation to solve for RfR_f.

    Subtract 1 from both sides:

    12−1=Rf1300 Ω12 - 1 = \frac{R_f}{1300 \, \Omega} 11=Rf1300 Ω11 = \frac{R_f}{1300 \, \Omega}

    Multiply both sides by 1300 Ω1300 \, \Omega:

    Rf=11×1300 ΩR_f = 11 \times 1300 \, \Omega
  4. Calculate the value of RfR_f.

    Rf=14300 ΩR_f = 14300 \, \Omega

    Convert to kilohms:

    Rf=14.3 kΩR_f = 14.3 \, \text{k}\Omega

    The value of the feedback resistor is 14.3 kΩ\text{14.3 k}\Omega.

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