In an `LCR` series ac circuit the voltage across `L,C` and `R` are `V_(1), V_(2)` and `V_(3)` respectively The voltage of the source is .

Options

A. equal to `V_(1)+V_(2)+V_(3)`
B. equal to `V_(1)-V_(2)+V_(3)`
C. more than `V_(1)+V_(2)+V_(3)`
D. none of these is ture

Answer

To find the voltage of the source in an LCR series AC circuit, we can use the relationship between the voltages across the inductor (L), capacitor (C), and resistor (R). The voltages across these components are represented as \( V_1 \), \( V_2 \), and \( V_3 \) respectively.

### Step-by-Step Solution:

1. **Identify the voltages across each component**:
- Let \( V_L = V_1 \) (voltage across the inductor)
- Let \( V_C = V_2 \) (voltage across the capacitor)
- Let \( V_R = V_3 \) (voltage across the resistor)

2. **Understand the phasor relationship**:
- In an LCR series circuit, the voltages do not simply add up algebraically due to their phase differences. The voltage across the inductor and capacitor are out of phase by 180 degrees.

3. **Apply the formula for the total voltage**:
- The total voltage of the source \( V \) can be calculated using the formula:
\[ V = \sqrt{(V_L - V_C)^2 + V_R^2} \]
- This formula accounts for the phase difference between the voltages across the inductor and capacitor.

4. **Substitute the values**:
- Substitute \( V_L \), \( V_C \), and \( V_R \) into the formula:
\[ V = \sqrt{(V_1 - V_2)^2 + V_3^2} \]

5. **Conclusion**:
- The voltage of the source in the LCR series AC circuit is given by:
\[ V = \sqrt{(V_1 - V_2)^2 + V_3^2} \]