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 root mean square (rms) value of the instantaneous current given by the equation \( i = \sqrt{2} \sin(50t + \frac{\pi}{4}) \), we can follow these steps:

### Step 1: Identify the Peak Current
The given equation for the instantaneous current is:
\[ i = \sqrt{2} \sin(50t + \frac{\pi}{4}) \]
In this equation, the term \(\sqrt{2}\) represents the peak current, denoted as \(I_0\).

### Step 2: Use the Formula for RMS Value
The rms value of an alternating current is given by the formula:
\[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \]
where \(I_0\) is the peak current.

### Step 3: Substitute the Peak Current into the RMS Formula
From Step 1, we have \(I_0 = \sqrt{2}\). Now we can substitute this value into the rms formula:
\[ I_{\text{rms}} = \frac{\sqrt{2}}{\sqrt{2}} \]

### Step 4: Simplify the Expression
Now, simplify the expression:
\[ I_{\text{rms}} = 1 \]

### Conclusion
Thus, the rms value of the current is:
\[ I_{\text{rms}} = 1 \text{ A} \]

### Final Answer
The rms value of the current is \(1 \text{ A}\).

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