Topic: Analog Circuits
Determine output voltage 'Vo' for below circuit where $V_{in}=\text{Sin}(100\pi t)$
- A. 2 Sin (100\pi t)
- B. 2 Cos (100\pi t) (as visually deduced from standard pairs, text partially obscured)
- C. Sin (200\pi t)
- D. 0.5 Sin (100\pi t)
Answer: B. 2 Cos (100\pi t) (as visually deduced from standard pairs, text partially obscured)
Explanation: The circuit shown is an inverting op-amp integrator with a capacitor in the feedback loop. The transfer function in the time domain is $V_{out}(t) = -\frac{1}{RC} \int V_{in}(t) dt$. Given the input is a sine wave ($V_{in} = \sin(100\pi t)$), integrating it produces a negative cosine wave, and the inverting nature of the amplifier flips it to a positive cosine wave. Thus, the output must be a cosine function, pointing to option (b).