Question

The dc component, fundamental frequency content in the following voltage signal is: V(ωt)=5+325sin(314t)+10sin(628t)

a. 5∨ and 50 Hz
b. 325 and 314
c. 0 and 314
d. 10 and 50

Answer 1

The DC component of the signal V(ωt)=5+325sin(314t)+10sin(628t) is 5 V and the fundamental frequency content of the signal is 50 Hz.

Step-by-step explanation:

The DC component and fundamental frequency content in the voltage signal V(ωt)=5+325sin(314t)+10sin(628t) are asked in the question.

The DC component is the part of the signal that does not change with time and is directly seen as the constant term in the equation. In this case, the constant term is 5 V.

The fundamental frequency is determined by the first harmonic (sine term) present in the signal. The angular frequency ω for the fundamental frequency is given by the first sine term's argument coefficient, which is 314t, where t is in seconds. To find the frequency in Hz, we divide the angular frequency by 2π, which gives us:

f = ω/(2π) = 314/(2π) ≈ 50 Hz

So, the DC component is 5 V and the fundamental frequency is 50 Hz.