Q1- An AC voltage is given below: V(t)=10+20cos(314t) Please find the average and RMS values of V(t)

Question

Answer 1

To find the average and RMS values of the given AC voltage

, we can use the following formulas:1. Average value:The average value of a periodic waveform over one complete cycle is given by the formula:

where

is the period of the waveform.In this case, the period

can be found by looking at the argument of the cosine function, which is

. Since the cosine function has a period of

, we can equate

to find the period:

Now, we can calculate the average value:

Evaluating the integral, we get:

Since the integral of

over one period is zero, we have:

2. RMS value:The RMS (Root Mean Square) value of a periodic waveform is given by the formula:

In this case, we can calculate the RMS value:

Expanding the square and evaluating the integral, we get:

Since the integral of

over one period is zero, we have:

We can use the identity

to simplify the integral:

Evaluating the integral, we get:

Since the integral of

over one period is zero, we have:

$\text{RMS value

Soru