Calculate the root mean square value of current if the instantaneous current in a circuit connected across an AC source is given by I = 5 sin 31.4 t.

Answer

To calculate the root mean square (RMS) value of the current given the instantaneous current \( I(t) = 5 \sin(31.4 t) \), we can follow these steps:

### Step 1: Identify the Peak Value
The instantaneous current is given by the equation:
\[ I(t) = I_0 \sin(\omega t) \]
where \( I_0 \) is the peak (maximum) value of the current. From the equation \( I(t) = 5 \sin(31.4 t) \), we can identify:
\[ I_0 = 5 \, \text{A} \]

### Step 2: Use the RMS Formula
The RMS value of an alternating current is calculated using the formula:
\[ I_{\text{RMS}} = \frac{I_0}{\sqrt{2}} \]
Substituting the value of \( I_0 \):
\[ I_{\text{RMS}} = \frac{5}{\sqrt{2}} \]

### Step 3: Calculate the RMS Value
Now, we can calculate \( I_{\text{RMS}} \):
\[ I_{\text{RMS}} = \frac{5}{\sqrt{2}} \approx \frac{5}{1.414} \approx 3.535 \, \text{A} \]

### Final Answer
Thus, the root mean square value of the current is:
\[ I_{\text{RMS}} \approx 3.54 \, \text{A} \]

---