A resistor `R` and the capacitor `C` are connected in series across an ac source of rms voltage `5V` if the rms voltage across `C` is `3V` then that across `R` is .

Options

A. `1V`
B. `2V`
C. `3V`
D. `4V`

Explanation

To solve the problem, we need to find the voltage across the resistor \( R \) when it is connected in series with a capacitor \( C \) across an AC source. Given the RMS voltage across the AC source is \( 5V \) and the RMS voltage across the capacitor \( C \) is \( 3V \), we can use the following steps:

### Step-by-Step Solution:

1. **Understand the Circuit Configuration**:
- The resistor \( R \) and capacitor \( C \) are connected in series across an AC source.
- The total RMS voltage \( V_{\text{RMS}} \) across the series circuit is given as \( 5V \).
- The voltage across the capacitor \( V_C \) is given as \( 3V \).

2. **Use the Voltage Relationship in Series Circuits**:
- In a series circuit, the total voltage is the sum of the voltages across each component:
\[ V_{\text{RMS}} = V_R + V_C \]
- Rearranging this gives us the voltage across the resistor \( R \):
\[ V_R = V_{\text{RMS}} - V_C \]

3. **Substitute the Known Values**:
- Substitute \( V_{\text{RMS}} = 5V \) and \( V_C = 3V \) into the equation:
\[ V_R = 5V - 3V \]

4. **Calculate the Voltage Across the Resistor**:
- Performing the subtraction:
\[ V_R = 2V \]

5. **Conclusion**:
- The voltage across the resistor \( R \) is \( 2V \).

### Final Answer:
The voltage across the resistor \( R \) is \( 2V \).