In an `LCR` series circuit the rms voltages across `R,L` and `C` are foundd to be `10 V, 10 V` and `20 V` respectively. The rms voltage across the entire combination is

Options

A. `30 V`
B. `1 V`
C. `20 V`
D. `10 sqrt(2) V`

Explanation

To find the rms voltage across the entire LCR series circuit, we can use the relationship between the voltages across the resistor (R), inductor (L), and capacitor (C). The formula for the total rms voltage in an LCR series circuit is given by:

\[ V_{rms} = \sqrt{V_R^2 + (V_L - V_C)^2} \]

### Step-by-step Solution:

1. **Identify the given values:**
- 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. **Substitute the values into the formula:**
\[ V_{rms} = \sqrt{V_R^2 + (V_L - V_C)^2} \]
\[ V_{rms} = \sqrt{(10)^2 + (10 - 20)^2} \]

3. **Calculate \( V_R^2 \):**
\[ V_R^2 = 10^2 = 100 \]

4. **Calculate \( (V_L - V_C)^2 \):**
\[ V_L - V_C = 10 - 20 = -10 \]
\[ (V_L - V_C)^2 = (-10)^2 = 100 \]

5. **Combine the results:**
\[ V_{rms} = \sqrt{100 + 100} = \sqrt{200} \]

6. **Simplify the square root:**
\[ V_{rms} = \sqrt{200} = 10\sqrt{2} \, V \]

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

---