A resistor and a capacitor are connected in series with an a.c. source. If the potential drop across the capacitor is 5 V and that across resistor is 12 V, applied voltage is

Options

A. 13V
B. 17 V
C. 5 V
D. 12 V

Explanation

To solve the problem, we need to find the applied voltage (V) across a resistor (R) and a capacitor (C) connected in series with an AC source. We know the potential drops across the capacitor (Vc) and the resistor (Vr).

### Step-by-Step Solution:

1. **Identify the given values:**
- Voltage across the capacitor, \( V_c = 5 \, \text{V} \)
- Voltage across the resistor, \( V_r = 12 \, \text{V} \)

2. **Understand the relationship in a series RC circuit:**
- In a series circuit with an AC source, the total voltage (V) is the vector sum of the voltages across the resistor and capacitor. This can be represented using the Pythagorean theorem because the voltages are 90 degrees out of phase.

3. **Apply the Pythagorean theorem:**
- The total voltage \( V \) can be calculated using the formula:
\[ V = \sqrt{V_r^2 + V_c^2} \]

4. **Substitute the known values into the equation:**
- Substitute \( V_r = 12 \, \text{V} \) and \( V_c = 5 \, \text{V} \):
\[ V = \sqrt{(12)^2 + (5)^2} \]
\[ V = \sqrt{144 + 25} \]
\[ V = \sqrt{169} \]

5. **Calculate the result:**
- Taking the square root:
\[ V = 13 \, \text{V} \]

6. **Conclusion:**
- The applied voltage across the series combination of the resistor and capacitor is \( 13 \, \text{V} \).

### Final Answer:
The applied voltage is \( 13 \, \text{V} \).