An AC voltage source has an output of V = 200 sin `2 pi ft`. This source is connected to a `100 Omega` resistor. RMS current in the resistance is

Options

A. 1.41 A
B. 2.41 A
C. 3.41 A
D. 0.71 A

Answer

To find the RMS current in the resistor connected to the AC voltage source, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given voltage equation**:
The AC voltage source is given by:
\[ V(t) = 200 \sin(2 \pi f t) \]
Here, \( V_0 = 200 \) volts is the peak voltage.

2. **Calculate the RMS voltage**:
The RMS (Root Mean Square) value of an AC voltage is given by the formula:
\[ V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \]
Substituting the peak voltage:
\[ V_{\text{rms}} = \frac{200}{\sqrt{2}} = 100\sqrt{2} \text{ volts} \]

3. **Use Ohm's Law to find the RMS current**:
The RMS current \( I_{\text{rms}} \) through a resistor can be calculated using Ohm's Law:
\[ I_{\text{rms}} = \frac{V_{\text{rms}}}{R} \]
where \( R = 100 \, \Omega \) (the resistance). Substituting the values:
\[ I_{\text{rms}} = \frac{100\sqrt{2}}{100} = \sqrt{2} \text{ amperes} \]

4. **Calculate the numerical value of RMS current**:
The numerical value of \( \sqrt{2} \) is approximately \( 1.414 \):
\[ I_{\text{rms}} \approx 1.414 \text{ amperes} \]

### Final Answer:
The RMS current in the resistance is approximately \( 1.414 \, \text{A} \).

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