In an `AC` circuit with voltage `V` and current `I`, the power dissipated is

Options

A. Depends on the phase between `V and I`
B. `(1)/(sqrt2)Vi`
C. `(1)/(2) Vi `
D. `vi`

Answer

To find the power dissipated in an AC circuit with voltage \( V \) and current \( I \), we can follow these steps:

### Step 1: Understand the Basics of AC Power
In an AC circuit, the power dissipated is not simply the product of voltage and current. Instead, it depends on the phase difference between the voltage and current.

### Step 2: Identify the RMS Values
The voltage \( V \) and current \( I \) in AC circuits are often expressed in terms of their root mean square (RMS) values. The RMS value of voltage is denoted as \( V_{rms} \) and that of current as \( I_{rms} \).

### Step 3: Use the Power Formula
The formula for the average power \( P \) dissipated in an AC circuit is given by:
\[ P = V_{rms} \cdot I_{rms} \cdot \cos \theta \]
where \( \theta \) is the phase difference between the voltage and current.

### Step 4: Analyze the Options
Now, let's analyze the options provided in the question:
1. The power depends on the phase between \( V \) and \( I \).
2. \( \frac{V I}{\sqrt{2}} \)
3. \( \frac{1}{2} V I \)
4. \( V I \)

From the formula derived in Step 3, we can see that the power indeed depends on the phase difference, which makes option 1 correct. The other options do not account for the phase difference and are not correct.

### Conclusion
Thus, the power dissipated in an AC circuit is given by the formula \( P = V_{rms} \cdot I_{rms} \cdot \cos \theta \), and the correct answer is option 1.

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