The current and voltage functions in an `AC` circuit are
`i=100 sin 100 tmA, V=100sin(100t+pi/3)V`
The power disspitated in the circuit is

Options

A. `10^4 Watt`
B. `2.5 Watt`
C. `5 Watt`
D. `10 Watt`

Explanation

To find the power dissipated in the AC circuit, we will follow these steps:

### Step 1: Identify the given functions
The current and voltage functions are given as:
- \( i(t) = 100 \sin(100t) \) mA
- \( V(t) = 100 \sin(100t + \frac{\pi}{3}) \) V

### Step 2: Determine the RMS values of current and voltage
The RMS (Root Mean Square) values for sinusoidal functions are calculated as follows:
- \( I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \)
- \( V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \)

Where \( I_0 \) and \( V_0 \) are the peak values of current and voltage, respectively.

From the given functions:
- The peak current \( I_0 = 100 \) mA
- The peak voltage \( V_0 = 100 \) V

Calculating the RMS values:
- \( I_{\text{rms}} = \frac{100 \text{ mA}}{\sqrt{2}} = \frac{100 \times 10^{-3}}{\sqrt{2}} \) A
- \( V_{\text{rms}} = \frac{100 \text{ V}}{\sqrt{2}} \) V

### Step 3: Calculate the phase difference
The phase difference \( \phi \) between the current and voltage is given as:
- \( \phi = \frac{\pi}{3} \)

### Step 4: Use the power formula
The power dissipated in the circuit can be calculated using the formula:
\[ P = V_{\text{rms}} \times I_{\text{rms}} \times \cos(\phi) \]

### Step 5: Substitute the values
Substituting the values we calculated:
- \( V_{\text{rms}} = \frac{100}{\sqrt{2}} \) V
- \( I_{\text{rms}} = \frac{100 \times 10^{-3}}{\sqrt{2}} \) A
- \( \cos(\frac{\pi}{3}) = \frac{1}{2} \)

Now substituting these into the power formula:
\[ P = \left(\frac{100}{\sqrt{2}}\right) \times \left(\frac{100 \times 10^{-3}}{\sqrt{2}}\right) \times \frac{1}{2} \]

### Step 6: Simplify the expression
Calculating the expression:
\[ P = \frac{100 \times 100 \times 10^{-3}}{2 \times 2} = \frac{10000 \times 10^{-3}}{4} = \frac{10}{4} = 2.5 \text{ W} \]

### Conclusion
The power dissipated in the circuit is:
\[ P = 2.5 \text{ W} \]

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