In a series resonant circuit, the `AC` voltage across resistance `R`, inductance `L`, and capacitance `C` are `5V,10V` and `10V` respectively. The `AC` voltage applied to the circuit will be

Options

A. `20 V`
B. `10 V`
C. `5 V`
D. `25 V`

Explanation

To find the AC voltage applied to the series resonant circuit with given voltages across the resistance (R), inductance (L), and capacitance (C), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Voltages**:
- Voltage across Resistance (Vr) = 5V
- Voltage across Inductance (VL) = 10V
- Voltage across Capacitance (VC) = 10V

2. **Understand the Phase Relationships**:
- In a series RLC circuit, the current (I) is the same through all components.
- The voltage across the resistor (Vr) is in phase with the current.
- The voltage across the inductor (VL) leads the current by 90 degrees.
- The voltage across the capacitor (VC) lags the current by 90 degrees.

3. **Represent the Voltages as Vectors**:
- Since Vr is in phase with I, we can represent it along the horizontal axis.
- VL will be represented as a vector pointing upwards (leading).
- VC will be represented as a vector pointing downwards (lagging).

4. **Calculate the Resultant Voltage**:
- The voltages across L and C are equal in magnitude but opposite in direction (10V each).
- Therefore, they will cancel each other out:
\[ VL + VC = 10V - 10V = 0V \]
- The total voltage (V) applied to the circuit will then be:
\[ V = Vr + (VL + VC) = 5V + 0V = 5V \]

5. **Conclusion**:
- The AC voltage applied to the circuit is 5V.

### Final Answer:
The AC voltage applied to the circuit is **5V**.