In a L - C - R series AC circuit, the voltage across each of the component L, C and R is 50 V. The voltage across the L -R combination will be:

Options

A. 50 V
B. `50sqrt(2)` V
C. 100 V
D. 0 V

Explanation

To solve the problem, we need to find the voltage across the L-R combination in a series L-C-R circuit where the voltage across each component (L, C, and R) is given as 50 V.

### Step-by-Step Solution:

1. **Understanding the Circuit**:
In a series L-C-R circuit, the voltage across each component can be represented as:
- Voltage across the inductor (L): \( V_L = 50 \, V \)
- Voltage across the capacitor (C): \( V_C = 50 \, V \)
- Voltage across the resistor (R): \( V_R = 50 \, V \)

2. **Voltage Relationships**:
In a series circuit, the total voltage across the circuit is the vector sum of the voltages across each component. The voltages across the inductor and capacitor are out of phase by 90 degrees, while the voltage across the resistor is in phase with the total current.

3. **Using Phasor Representation**:
Since \( V_L \) and \( V_C \) are 90 degrees out of phase, we can represent them as vectors:
- \( V_L \) is along the positive y-axis.
- \( V_R \) is along the x-axis.

4. **Calculating the Voltage Across L-R Combination**:
The voltage across the L-R combination can be calculated using the Pythagorean theorem because \( V_L \) and \( V_R \) are perpendicular to each other:
\[ V_{LR} = \sqrt{V_L^2 + V_R^2} \]
Substituting the values:
\[ V_{LR} = \sqrt{(50 \, V)^2 + (50 \, V)^2} \]
\[ V_{LR} = \sqrt{2500 + 2500} \]
\[ V_{LR} = \sqrt{5000} \]
\[ V_{LR} = 50 \sqrt{2} \, V \]

5. **Final Calculation**:
To express \( 50 \sqrt{2} \) in decimal form:
\[ V_{LR} \approx 50 \times 1.414 \approx 70.7 \, V \]

Thus, the voltage across the L-R combination is approximately **70.7 V**.