r.m.s. value of current `i=3+4 sin (omega t+pi//3)` is:

Options

A. `5 A`
B. `sqrt17 A`
C. `5/sqrt2 A`
D. `7/sqrt2 A`

Explanation

To find the root mean square (r.m.s.) value of the current given by the equation \( i = 3 + 4 \sin(\omega t + \frac{\pi}{3}) \), we will follow these steps:

### Step 1: Identify the expression for the current
The given current is:
\[ i = 3 + 4 \sin(\omega t + \frac{\pi}{3}) \]

### Step 2: Square the current expression
To find the r.m.s. value, we first need to square the current:
\[ i^2 = (3 + 4 \sin(\omega t + \frac{\pi}{3}))^2 \]
Using the expansion of \( (a + b)^2 = a^2 + 2ab + b^2 \), we get:
\[ i^2 = 3^2 + 2 \cdot 3 \cdot 4 \sin(\omega t + \frac{\pi}{3}) + (4 \sin(\omega t + \frac{\pi}{3}))^2 \]
Calculating each term:
\[ = 9 + 24 \sin(\omega t + \frac{\pi}{3}) + 16 \sin^2(\omega t + \frac{\pi}{3}) \]

### Step 3: Simplify the expression for \( i^2 \)
Now, we can simplify \( i^2 \):
\[ i^2 = 9 + 24 \sin(\omega t + \frac{\pi}{3}) + 16 \sin^2(\omega t + \frac{\pi}{3}) \]

### Step 4: Calculate the average of \( i^2 \)
To find the r.m.s. value, we need to calculate the average of \( i^2 \) over one complete cycle. The average of \( \sin^2 \) over one cycle is \( \frac{1}{2} \):
\[ \text{Average of } i^2 = 9 + 24 \cdot 0 + 16 \cdot \frac{1}{2} \]
\[ = 9 + 0 + 8 = 17 \]

### Step 5: Calculate the r.m.s. value
The r.m.s. value is the square root of the average of \( i^2 \):
\[ I_{\text{rms}} = \sqrt{17} \]

### Final Answer
Thus, the r.m.s. value of the current \( i \) is:
\[ \boxed{\sqrt{17}} \]