The peak value of Alternating current is `6`amp, then r.m.s. value of current will be

Options

A. 0.125
B. `3sqrt(3) A`
C. `3sqrt(2) A`
D. `2sqrt(3)`A

Answer

To find the root mean square (RMS) value of an alternating current (AC) given its peak value, we can use the relationship between the peak current (I₀) and the RMS current (I_rms). The formula is:

\[ I_{rms} = \frac{I_0}{\sqrt{2}} \]

### Step-by-Step Solution:

1. **Identify the Peak Value**:
The peak value of the alternating current is given as \( I_0 = 6 \, \text{A} \).

2. **Apply the RMS Formula**:
Use the formula for RMS current:
\[ I_{rms} = \frac{I_0}{\sqrt{2}} \]

3. **Substitute the Peak Value**:
Substitute \( I_0 \) into the formula:
\[ I_{rms} = \frac{6}{\sqrt{2}} \]

4. **Calculate the RMS Value**:
To simplify \( \frac{6}{\sqrt{2}} \), multiply the numerator and denominator by \( \sqrt{2} \):
\[ I_{rms} = \frac{6 \sqrt{2}}{2} = 3\sqrt{2} \, \text{A} \]

5. **Final Answer**:
Therefore, the RMS value of the current is:
\[ I_{rms} = 3\sqrt{2} \, \text{A} \approx 4.24 \, \text{A} \]