In the circuit shown below, assuming an ideal op-amp, for an input voltage \( V_{in} = 1 \, V \), the output voltage \( V_{out} = ? \, \) (in vol)
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In ideal op-amps, the output voltage is driven to a value that keeps the voltage difference between the inverting and non-inverting inputs at zero (virtual short concept).
Understanding the Ideal Op-Amp Circuit:
The given circuit involves an ideal operational amplifier (op-amp) with the following characteristics:
Infinite open-loop gain
Zero input current
Operating in a closed-loop (negative feedback) configuration
Key Principle:
In the linear region of operation, for an ideal op-amp:
\( V_+ = V_- \) due to the infinite gain and the presence of negative feedback.
Given:
The non-inverting input voltage is:
\( V_+ = V_{in} = 1 \, \text{V} \)
Since \( V_+ = V_- \), it follows that:
\( V_- = 1 \, \text{V} \)
Output Voltage:
As long as the op-amp remains in the linear region and is not saturated, the output adjusts such that the condition \( V_+ = V_- \) holds. Given the op-amp’s saturation limits of:
\( +15 \, \text{V} \) (positive rail)
\( -15 \, \text{V} \) (negative rail)
The output voltage must remain within these bounds. Since the input voltage and feedback maintain equilibrium at \( V_{out} = 1 \, \text{V} \), it does not reach saturation.
