If the input resistor of an inverting amplifier using OP-AMP is doubled and the feedback resistor remains the same, what happens to the magnitude of voltage gain?
It is halved
An inverting amplifier using an operational amplifier (OP-AMP) has a configuration where the voltage gain \(A_v\) is determined by the feedback resistor (\(R_f\)) and the input resistor (\(R_{in}\)). The formula for the voltage gain of an inverting amplifier is given by:
\(A_v = -\dfrac{R_f}{R_{in}}\)
Let's analyze what happens when the input resistor \(R_{in}\) is doubled, while the feedback resistor \(R_f\) remains unchanged.
- Initially, the voltage gain is:
\(A_v = -\dfrac{R_f}{R_{in}}\)
- If \(R_{in}\) is doubled, we have a new input resistor value of \(2R_{in}\). The modified voltage gain becomes:
\(A_v' = -\dfrac{R_f}{2R_{in}}\)
- Comparing the new gain \(A_v'\) with the original gain \(A_v\):
The ratio of the new gain to the original gain is:
\(\dfrac{A_v'}{A_v} = \dfrac{-\dfrac{R_f}{2R_{in}}}{-\dfrac{R_f}{R_{in}}} = \dfrac{1}{2}\)
This indicates that the new gain is half the original gain.
Therefore, when the input resistor of an inverting amplifier is doubled, the magnitude of the voltage gain is halved. Hence, the correct answer is: It is halved.
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