The instantaneous current in an AC circuit is l = `sqrt 2`sin(50 t + `pi` / 4 ) . The rms value of current is

Options

A. `sqrt 2`A
B. 50 A
C. 90 A
D. 1A

Explanation

To find the rms (root mean square) value of the current given in the AC circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Equation**:
The instantaneous current is given as:
\[ I(t) = \sqrt{2} \sin(50t + \frac{\pi}{4}) \]

2. **Compare with the Standard Form**:
The standard form of the instantaneous current in an AC circuit is:
\[ I(t) = I_0 \sin(\omega t + \phi) \]
where \(I_0\) is the peak (maximum) current, \(\omega\) is the angular frequency, and \(\phi\) is the phase angle.

3. **Determine the Peak Current**:
By comparing the two equations, we can see that:
\[ I_0 = \sqrt{2} \]

4. **Calculate the RMS Value**:
The rms value of the current is calculated using the formula:
\[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \]
Substituting the value of \(I_0\):
\[ I_{\text{rms}} = \frac{\sqrt{2}}{\sqrt{2}} = 1 \text{ A} \]

5. **Final Answer**:
Therefore, the rms value of the current is:
\[ I_{\text{rms}} = 1 \text{ A} \]