Question

if a voltage v(t) = 150sinwt in volts at an operating frequency of 100hz. determine the I. dc value ii.rms value iii.period of the voltage signal​

Answer 1

(a) The dc value is 95.5 volts

(b) The rms value is 106.1 volts

(c) The period is 0.01s

Step-by-step explanation:

Given

`V(t) = 150\sin(wt)`

`f = 100Hz`

Solving (a): The dc value

`V(t) = 150\sin(wt)` implies that

`V_(max) = 150`

So, the dc value is:

`V = (2)/(\pi) * V_(max)`

`V = (2)/(\pi) * 150`

`V = (300)/(\pi)`

`V = 95.5V`

Solving (b): The RMS value

This is calculated as:

`V_(rms) = (1)/(\sqrt 2) * V_(max)`

So, we have:

`V_(rms) = (1)/(\sqrt 2) * 150`

`V_(rms) = (150)/(\sqrt 2)`

`V_(rms) = 106.1V\\`

Solving (c): The period

This is calculated as:

`T = (1)/(f)`

So, we have:

`T = (1)/(100Hz)`

`T = 0.01s`