The instantaneous current in an A.C. circuit is given by `I= 2 sin (omega t+theta)` ampere. The r.m.s. value of the current is

Options

A. 2 ampere
B. `2sqrt(2)` ampere
C. `sqrt(2)` ampere
D. `1/(sqrt(2))` ampere

Answer

To find the root mean square (r.m.s.) value of the instantaneous current given by the equation \( I = 2 \sin(\omega t + \theta) \) ampere, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Peak Current**:
The given equation for the instantaneous current is \( I = 2 \sin(\omega t + \theta) \). In this equation, the coefficient of the sine function represents the peak current (\( I_0 \)).
\[ I_0 = 2 \text{ A} \]

2. **Use the Formula for r.m.s. Current**:
The formula for the root mean square (r.m.s.) value of an alternating current is given by:
\[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \]

3. **Substitute the Peak Current into the Formula**:
Now, substitute the value of \( I_0 \) into the r.m.s. formula:
\[ I_{\text{rms}} = \frac{2}{\sqrt{2}} \]

4. **Simplify the Expression**:
Simplifying the expression gives:
\[ I_{\text{rms}} = \frac{2}{\sqrt{2}} = \frac{2 \sqrt{2}}{2} = \sqrt{2} \text{ A} \]

5. **Final Result**:
Therefore, the r.m.s. value of the current is:
\[ I_{\text{rms}} = \sqrt{2} \text{ A} \]