Question

For low frequency filters, the corresponding time constants for LFF cutoff frequency of 3 Hz would be _____________.

1) 1/3 s
2) 1/6 s
3) 1/9 s
4) 1/12 s

Answer 1

The corresponding time constant for a low frequency filter with a 3 Hz cutoff frequency is approximately 1/18 seconds, which is closest to the calculated value of 0.053 seconds.

Step-by-step explanation:

For low frequency filters like the ones being discussed, the corresponding time constant (T) is related to the cutoff frequency (f) by the formula T = 1/(2πf). To find the time constant for a low frequency filter (LFF) with a cutoff frequency of 3 Hz, substitute the value of f = 3 Hz into the formula:

T = 1/(2π × 3 Hz) = 1/(6.2832 × 3) = 1/18.8496 ≈ 0.053 seconds.

The closest answer from the given options is 1/18 s as it is the closest approximation to the calculated value, converting to approximately 0.056 seconds, which is in the range of μF and mH necessary to achieve the desired cutoff for filtering applications.