If reading of an ammeter is 10 A, the peak value of current is

Options

A. `10/(sqrt(2))A`
B. `5/(sqrt(2))A`
C. `20sqrt(2)A`
D. `10sqrt(2)A`

Answer

To find the peak value of current (I₀) when the reading of an ammeter is given as 10 A, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Measurement**: The ammeter measures the effective value of current, which is the root mean square (RMS) value. In this case, the RMS value (Iₘₛ) is given as 10 A.

2. **Use the Relationship Between RMS and Peak Current**: The relationship between the RMS value (Iₘₛ) and the peak value (I₀) of an alternating current is given by the formula:
\[ Iₘₛ = \frac{I₀}{\sqrt{2}} \]

3. **Substitute the RMS Value**: We can substitute the given RMS value into the equation:
\[ 10 A = \frac{I₀}{\sqrt{2}} \]

4. **Cross-Multiply to Solve for Peak Current**: To find the peak current (I₀), we can rearrange the equation:
\[ I₀ = 10 A \times \sqrt{2} \]

5. **Calculate the Peak Current**: Now, we can calculate the peak current:
\[ I₀ = 10\sqrt{2} A \]

6. **Final Answer**: Therefore, the peak value of current is:
\[ I₀ = 10\sqrt{2} A \]

### Conclusion:
The peak value of the current when the ammeter reads 10 A is \( 10\sqrt{2} \) A.

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