If instantaneous current is given by `i=4 cos(omega t + varphi)` amperes, then the `r.m.s.` value of current is

Options

A. `4` ampere
B. `2sqrt(2)` ampere
C. `4sqrt(2)` ampere
D. Zero ampere

Explanation

To find the root mean square (RMS) value of the given instantaneous current \( i = 4 \cos(\omega t + \varphi) \) amperes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Maximum Current**:
The given instantaneous current can be expressed in the form \( i = I_{\text{max}} \cos(\omega t + \varphi) \). From the equation, we can see that:
\[ I_{\text{max}} = 4 \, \text{amperes} \]

2. **Use the Formula for RMS Current**:
The RMS value of an alternating current is given by the formula:
\[ I_{\text{RMS}} = \frac{I_{\text{max}}}{\sqrt{2}} \]

3. **Substitute the Maximum Current into the Formula**:
Now, substituting \( I_{\text{max}} = 4 \) amperes into the RMS formula:
\[ I_{\text{RMS}} = \frac{4}{\sqrt{2}} \]

4. **Simplify the Expression**:
To simplify \( \frac{4}{\sqrt{2}} \):
\[ I_{\text{RMS}} = \frac{4 \sqrt{2}}{2} = 2\sqrt{2} \, \text{amperes} \]

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

### Summary:
The RMS value of the instantaneous current \( i = 4 \cos(\omega t + \varphi) \) is \( 2\sqrt{2} \) amperes.