A complex current wave is given by `i=5+5sin100omegatA`. Its average value over one time period is given as

Options

A. 10A
B. 5A
C. `sqrt 50 ` A
D. 0

Answer

To find the average value of the complex current wave given by \( i = 5 + 5 \sin(100 \omega t) \) over one time period, we can follow these steps:

### Step 1: Identify the components of the current wave
The given current wave can be split into two parts:
- A constant part: \( 5 \)
- An oscillating part: \( 5 \sin(100 \omega t) \)

### Step 2: Calculate the average value of the oscillating part
The average value of the sine function over one complete cycle (time period) is zero. Mathematically, this can be expressed as:
\[ \text{Average value of } \sin(100 \omega t) \text{ over one period} = 0 \]

### Step 3: Calculate the average value of the constant part
The average value of a constant over any interval is simply the constant itself. Therefore, the average value of the constant part \( 5 \) is:
\[ \text{Average value of } 5 = 5 \]

### Step 4: Combine the average values
The total average value of the current \( i \) over one time period is the sum of the average values of its components:
\[ \text{Average value of } i = \text{Average value of } 5 + \text{Average value of } 5 \sin(100 \omega t) = 5 + 0 = 5 \]

### Conclusion
Thus, the average value of the complex current wave \( i = 5 + 5 \sin(100 \omega t) \) over one time period is:
\[ \text{Average value} = 5 \, \text{A} \]

### Final Answer
The average value over one time period is \( 5 \, \text{A} \).