Discussion
An integrator contains 100 kΩ and 1 μF capacitor. If the voltage applied to the integrator is 1 Volt, what is the output of the integrator after 1 sec ?
Answer: A
The output is 10 V in magnitude.
An op-amp integrator gives \(v_{o} = -\frac{1}{RC}\int v_{i}\, dt\). With a constant input the output ramps linearly:
\[ \begin{aligned} RC &= 100 \times 10^{3} \times 1 \times 10^{-6} = 0.1\ \text{s} \\ |v_{o}| &= \frac{1 \times 1}{0.1} = 10\ \text{V} \end{aligned} \]
For the usual inverting integrator the output is -10 V, which is within the swing of a typical supply. 5 V and 15 V come from wrong time constants, and 0 V would mean no integration at all.
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