A time constant of 0.5 sec is associated with which filter type?

The time constant of a filter is a critical parameter that indicates how quickly the filter reacts to changes in the input signal. In this case, a time constant of 0.5 seconds suggests that the filter is responding to frequencies that are relatively low, as longer time constants correspond to the attenuation of higher frequencies.

The filter associated with a time constant of 0.5 seconds is a high-pass filter with a cutoff frequency. The cutoff frequency can be calculated from the time constant using the relationship ( f_c = \frac{1}{2\pi \times \tau} ), where ( \tau ) is the time constant. In this scenario, using the time constant of 0.5 seconds, we can derive that the cutoff frequency aligns with a value indicative of a high-pass filter, which is more effective at passing high-frequency signals while attenuating lower ones.

The other choices are associated with different filter characteristics or configurations, which do not correspond to a time constant of 0.5 seconds. This reinforces that the correct association with a high-pass filter and the calculated cutoff frequency distinguishes option D as the correct answer.