Question

6. The current and voltage in a circuit are given by
I= 3.5 sin (628t + 30°) ampere, V=28 sin (628t-30°)
volt. Determine (i) peak value, (ii) root-mean-square
value, (iii) time-period of the current and (iv) phase
difference between voltage and current.
0

Answer 1

Explanation:

I hope it's helpful for you

Answer 2

Given:-

I= 3.5 sin (628t + 30°) ampere, V=28 sin (628t-30°)

To find:-

(i) peak value, (ii) root-mean-square

value, (iii) time-period of the current and (iv) phase

difference between voltage and current.

Solution:-

According to the given equations,

I= 3.5 sin (628t + 30°) ampere, V=28 sin (628t-30°)

To find the peak value of current use the formulae,

i = io*sin(w*t + Ф)

v = vo*sin(w*t - Ф)

Now compare the equation with the current equation and hence we get the values as,

io = 3.5 A

To find irms value use the formula,

irms= io/$\sqrt{2}$

= 3.5/$\sqrt{2}$

= 2.47 A.

Now find T,

Compare given equation with the standard equations we will get, W = 628.

Current,

W = 2π/T

T =  2π/628

= 2*22/628*7

= 0.0108

The phase difference is calculated as,

Фi for current and Фv for voltage,

phase difference ΔФ = Фi - Фv

= 30-(-30)

= 60.

The required ste of answers are  io = 3.5 A, irms= 2.47 A, T= 0.0108,ΔФ = 60 respectively.