The peak voltage in a `220 V AC` source is

Options

A. `220 V`
B. about `160 V`
C. about `310 V`
D. `440 V`

Answer

To find the peak voltage in a `220 V AC` source, we can follow these steps:

### Step 1: Understand the relationship between RMS voltage and peak voltage
The relationship between the peak voltage (V₀) and the RMS voltage (V_RMS) is given by the formula:
\[ V₀ = \sqrt{2} \times V_{RMS} \]

### Step 2: Identify the RMS voltage
In this case, the RMS voltage is given as:
\[ V_{RMS} = 220 \, V \]

### Step 3: Substitute the RMS voltage into the formula
Now, we can substitute the value of the RMS voltage into the formula to find the peak voltage:
\[ V₀ = \sqrt{2} \times 220 \]

### Step 4: Calculate the peak voltage
Calculating the value:
\[ V₀ = 1.414 \times 220 \]
\[ V₀ \approx 311.08 \, V \]

### Step 5: Round the answer
Rounding the result gives us:
\[ V₀ \approx 311.13 \, V \]

### Step 6: Compare with the options
From the options provided, we can see that the closest value to 311.13 V is approximately 310 V.

### Final Answer
Thus, the peak voltage in a `220 V AC` source is approximately **311 V**, and the correct option is **option 3**, which states that the peak voltage is about **310 V**.

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