Question

The Dimensions of the time constant are:
A) $[{M^0}{L^0}{T^0}]$
B) $[{M^0}{L^0}T]$
C) $[MLT]$
D) None of these.

Answer 1

In the time domain, a step answer to a step input or an impulse response to a Dirac delta function input is a typical alternative for examining the time response. The time constant in the frequency domain (for example, by looking at the Fourier transformation of the phase response, or by using a simple sinusoidal time function), also defines the bandwidth of a first-order time-increasing device, namely the frequency at which the signal output power decreases to half that of a low frequency.

The frequency response of different signal processing devices-cassette tapes, radio senders and receivers, recording and replaying equipment and Optical Filters-that are modelled or approximated by first-order LTI systems is often calculated by the time constant. Other examples include time constants used in control systems, mostly pneumatic rather than electrical for integral and derivative action controls.

Complete step by step solution:
Unit for time is second,
Therefore, the dimensions for time constant is $[{M^0}{L^0}T]$

Hence the correct option is B

Note: In the time domain, a step answer to a step input or an impulse response to a Dirac delta function input is a typical alternative for examining the time response. The time constant in the frequency domain (for example, by looking at the Fourier transformation of the phase response, or by using a simple sinusoidal time function), also defines the bandwidth of a first-order time-increasing device, namely the frequency at which the signal output power decreases to half that of a low frequency.