The average value of alternating current over a complete cycle is

Options

A. zero
B. 1 rms
C. ` (I ) / ( sqrt 2 ) `
D. ` 2I `

Explanation

To find the average value of alternating current (AC) over a complete cycle, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Alternating Current**:
- Alternating current varies with time, typically represented as a sine wave. The current changes direction periodically, alternating between positive and negative values.

2. **Graph Representation**:
- If we plot the current (i) against time (t), the graph will show a sine wave that oscillates above and below the time axis. The positive half of the cycle corresponds to the current flowing in one direction, and the negative half corresponds to the current flowing in the opposite direction.

3. **Complete Cycle Analysis**:
- A complete cycle of AC consists of both the positive and negative halves. For example, if the maximum current is \( I \), then during the positive half of the cycle, the current varies from 0 to \( I \) and back to 0, and during the negative half, it varies from 0 to -\( I \) and back to 0.

4. **Calculating Average Value**:
- The average value of a function over a complete cycle is given by the integral of the function over one complete cycle divided by the period of the cycle. However, for AC, since the positive and negative halves cancel each other out, the average value can also be intuitively understood.
- Mathematically, the average value \( \overline{i} \) over one complete cycle can be expressed as:
\[ \overline{i} = \frac{1}{T} \int_0^T i(t) \, dt \]
- Where \( T \) is the period of the cycle. Since the positive and negative areas under the curve are equal and opposite, the integral evaluates to zero.

5. **Conclusion**:
- Therefore, the average value of alternating current over a complete cycle is:
\[ \overline{i} = 0 \]

### Final Answer:
The average value of alternating current over a complete cycle is **0**.

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