For a low frequency filter (LFF), the time constant for a cutoff frequency of 3 Hz would be?

To determine the time constant for a low frequency filter (LFF) with a cutoff frequency of 3 Hz, it is important to understand the relationship between the cutoff frequency and the time constant. The formula that relates these two parameters is:

[ \tau = \frac{1}{2 \pi f_c} ]

where ( \tau ) is the time constant in seconds and ( f_c ) is the cutoff frequency in hertz.

Given a cutoff frequency of 3 Hz, you can plug the value into the formula:

[ \tau = \frac{1}{2 \pi (3)} ]

Calculating this gives:

[ \tau = \frac{1}{6.2832} \approx 0.15915 \text{ seconds} ]

Since the time constant related to a cutoff frequency of 3 Hz involves identifying the least duration for the filter to respond and settle, one must analyze how a lower cutoff frequency manifests in a longer time domain response.

However, if we analyze the cutoff frequency further in relation to the provided options, we unlock the understanding of the problem statement. The calculations associated with time constant suggest that it is necessary to convert to the proper values presented in the options.