Question

If a voltage v(t)=150sinwt in volts at an operating frequency of 100Hz. Determine the following:
i. DC value
ii. RMS value
iii. Period of the voltage signal

Answer 1

i. First, from the equation for the voltage we determine:

$V_{(t)}=150sin(\omega t)=V_{max}sin(\omega t)=V_{max}sin(200\pi t)$

$V_{max}=150\,V=\frac{\pi}{2}V_{average}=\sqrt{2}V_{RMS}$

$\implies V_{average} = \dfrac{2}{\pi}V_{max}=\frac{2}{\pi}(150\,V)=95.493\,V$ .

ii. Then, from what we stated before:

$V_{RMS}=\frac{1}{\sqrt{2}}V_{max}=\frac{150\,V}{\sqrt{2}}=106.066\,V$ .

iii. The period can be found with the frequency: $\omega=2\pi f=\dfrac{2\pi}{T}$

$\implies T=\cfrac{1}{f}=\cfrac{1}{100\,Hz}=0.01 \,s$ .

In conclusion, we found that the DC value is V_average=95.493 V, while the RMS value for the voltage is V_RMS=106.066 V and the period of the voltage signal T = 0.01 s.

Reference:

• Young, H. D., & Freedman, R. A. (2015). University Physics with Modern Physics and Mastering Physics (p. 1632). Academic Imports Sweden AB.