The r.m.s. voltage of domestic electricity supply is `220` volt. Electrical appliances should be designed to withstand an instantaneous voltage of

Options

A. `220V`
B. `311V`
C. `330V`
D. `440V`

Explanation

To determine the instantaneous voltage that electrical appliances should be designed to withstand, we can follow these steps:

### Step 1: Understand the relationship between RMS voltage and peak voltage
The RMS (Root Mean Square) voltage is related to the peak voltage (V_peak) in an AC circuit. The relationship is given by the formula:
\[ V_{rms} = \frac{V_{peak}}{\sqrt{2}} \]
This means that the peak voltage is \(\sqrt{2}\) times the RMS voltage.

### Step 2: Calculate the peak voltage
Given that the RMS voltage \(V_{rms}\) is 220 volts, we can rearrange the formula to find the peak voltage:
\[ V_{peak} = V_{rms} \times \sqrt{2} \]
Substituting the given value:
\[ V_{peak} = 220 \times \sqrt{2} \]

### Step 3: Evaluate \(\sqrt{2}\)
The value of \(\sqrt{2}\) is approximately 1.414. Thus, we can calculate:
\[ V_{peak} = 220 \times 1.414 \approx 311.08 \text{ volts} \]

### Step 4: Conclusion
Therefore, the electrical appliances should be designed to withstand an instantaneous voltage of approximately 311 volts.

### Final Answer
The instantaneous voltage that electrical appliances should be designed to withstand is approximately **311 volts**.

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