Question

A pulse waveform has a high time of $8\,{\text{ms}}$ and a pulse width of $32\,{\text{ms}}$. The duty cycle is
A. 25%
B. 50%
C. 1%
D. 100%

Answer 1

We can use the formula for the duty cycle of a pulse waveform. This formula gives the relation between the duty cycle of the pulse waveform, rise time of the pulse waveform and total time period of the pulse waveform. The high time of the pulse waveform is the rise time of the pulse waveform and pulse of the pulse waveform is the total rise time of the pulse waveform. We can calculate the required value of the duty cycle by substituting the given values in this equation.

Formula used:
The expression for the duty cycle is given by
${\text{duty cycle}} = \dfrac{{{\text{Rise time}}}}{{{\text{Total time period}}}} \times 100$ …… (1)

Complete Step by Step Answer:
We have given that the high time of a pulse waveform is $8\,{\text{ms}}$. The high time of the pulse waveform is the rise time of the pulse waveform.
${\text{Rise time}} = 8\,{\text{ms}}$
We have also given that the pulse width of the pulse waveform is $32\,{\text{ms}}$.The pulse width of a pulse waveform is the total time period of the pulse waveform.
${\text{Total time period}} = 32\,{\text{ms}}$

We have asked to calculate the duty cycle of the given pulse waveform.We can calculate the duty cycle of the given pulse waveform using equation (1).Substitute $8\,{\text{ms}}$ for rise time and $32\,{\text{ms}}$ for total time period in equation (1).
${\text{duty cycle}} = \dfrac{{8\,{\text{ms}}}}{{32\,{\text{ms}}}} \times 100$
$\Rightarrow {\text{duty cycle}} = \dfrac{1}{4} \times 100$
$\therefore {\text{duty cycle}} = 25\%$
Therefore, the duty cycle of the given pulse waveform is $25\%$.

Hence, the correct option is A.

Note: The students should not get confused between the given values as the given values are not with the same titles as that used in the formula for duty cycle. Also the students should keep in mind that there is no need to convert the units of the rise time and total time period of the pulse waveform in the SI system of units as the units of both quantities get cancelled and the final answer is a unitless quantity.