The electric current in AC circuit is given by the relation i =`3sinomegat + 4cosomegat`. The rms value of the current in the circuit in ampere is

Options

A. `5/sqrt(2)`
B. `5sqrt(2)`
C. `sqrt(2)/5`
D. `1/sqrt(2)`

Explanation

To find the RMS value of the current given by the equation \( i = 3 \sin(\omega t) + 4 \cos(\omega t) \), we can follow these steps:

### Step 1: Identify the components of the current
The current can be expressed as a combination of sine and cosine functions. Here, we have:
- \( I_1 = 3 \) (coefficient of \( \sin(\omega t) \))
- \( I_2 = 4 \) (coefficient of \( \cos(\omega t) \))

### Step 2: Calculate the peak current \( I_0 \)
The peak current \( I_0 \) can be calculated using the formula:
\[ I_0 = \sqrt{I_1^2 + I_2^2} \]
Substituting the values:
\[ I_0 = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{A} \]

### Step 3: Calculate the RMS value of the current
The RMS (Root Mean Square) value of the current is given by the formula:
\[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \]
Substituting the value of \( I_0 \):
\[ I_{\text{rms}} = \frac{5}{\sqrt{2}} \, \text{A} \]

### Conclusion
Thus, the RMS value of the current in the circuit is:
\[ I_{\text{rms}} = \frac{5}{\sqrt{2}} \, \text{A} \]

### Final Answer
The RMS value of the current in the circuit is \( \frac{5}{\sqrt{2}} \) A.

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