In an L-C-R circuit the AC voltage across R, L and C comes out as 10 V , 10 V and 20 V respectively . The voltage across the enter combination will be

Options

A. 30 V
B. `10sqrt(3)`V
C. 20 V
D. `10sqrt(2)`A

Answer

To find the voltage across the entire L-C-R circuit given the voltages across the resistor (R), inductor (L), and capacitor (C), we can use the following steps:

### Step-by-Step Solution:

1. **Identify the Given Voltages**:
- Voltage across the resistor, \( V_R = 10 \, V \)
- Voltage across the inductor, \( V_L = 10 \, V \)
- Voltage across the capacitor, \( V_C = 20 \, V \)

2. **Understand the Relationship**:
In an L-C-R circuit, the voltages across the components are not in phase. Therefore, we need to use the formula for the total voltage \( V \) across the combination:
\[ V = \sqrt{V_R^2 + (V_C - V_L)^2} \]

3. **Calculate \( V_C - V_L \)**:
\[ V_C - V_L = 20 \, V - 10 \, V = 10 \, V \]

4. **Substitute the Values into the Formula**:
Now substitute \( V_R \) and \( (V_C - V_L) \) into the formula:
\[ V = \sqrt{(10 \, V)^2 + (10 \, V)^2} \]

5. **Calculate Each Term**:
\[ (10 \, V)^2 = 100 \, V^2 \]
Therefore,
\[ V = \sqrt{100 \, V^2 + 100 \, V^2} = \sqrt{200 \, V^2} \]

6. **Final Calculation**:
\[ V = \sqrt{200} \, V = 10\sqrt{2} \, V \]

### Conclusion:
The voltage across the entire combination is \( 10\sqrt{2} \, V \).