Final answer:
An ideal op-amp differentiator with a 1-ms time constant should not have an output voltage that increases or decreases exponentially. Instead, it would be proportional to the rate of change of the input voltage, ideally zero for a constant input. Exponential behaviors are more associated with charging and discharging of capacitors. Therefore, the correct answer is c) The output voltage is constant.
Step-by-step explanation:
When discussing an op-amp differentiator with a 1-ms time constant, there are a few potential behaviors for the output voltage, depending on the input. However, none of them include an output that rises or decreases exponentially. An ideal differentiator would produce an output voltage that is proportional to the rate of change of the input voltage.
Thus, should the input be a constant voltage, the output would ideally be zero since there is no change. In practical scenarios, the output might display high-frequency noise or react to sudden changes in input voltage.
Exponential behaviors, typically described by an increasing or decreasing exponential function, are often seen in RC circuits during the charging or discharging of capacitors, respectively. During the charging of a capacitor, the voltage rises to 0.632 of its final value in each time constant period.
Conversely, when discharging a capacitor through a resistor, the voltage falls to 0.368 of its initial value in one time constant period. These are characteristic behaviors of exponential decay and exponential growth processes.