Calculate the potential across the capacitance if 50 V AC is applied across RC circuit and the rms voltage across the resistance is 40 V.

Options

A. 10 V
B. 20 V
C. 30 V
D. 40 V

Explanation

To solve the problem, we need to find the potential across the capacitance (Vc) in an RC circuit where a 50 V AC voltage is applied, and the RMS voltage across the resistance (Vr) is given as 40 V.

### Step-by-Step Solution:

1. **Understand the Circuit**:
- We have an RC circuit connected to an AC source of 50 V (RMS).
- The voltage across the resistor (Vr) is given as 40 V (RMS).

2. **Use the Phasor Relationship**:
- In an RC circuit, the total voltage (V) is related to the voltages across the resistor (Vr) and the capacitor (Vc) using the Pythagorean theorem because they are out of phase by 90 degrees:
\[ V^2 = V_r^2 + V_c^2 \]

3. **Substitute the Known Values**:
- We know:
- Total voltage, \( V = 50 \, V \)
- Voltage across the resistor, \( V_r = 40 \, V \)
- Substitute these values into the equation:
\[ 50^2 = 40^2 + V_c^2 \]

4. **Calculate the Squares**:
- Calculate \( 50^2 \) and \( 40^2 \):
\[ 2500 = 1600 + V_c^2 \]

5. **Rearrange the Equation**:
- To find \( V_c^2 \):
\[ V_c^2 = 2500 - 1600 \]
\[ V_c^2 = 900 \]

6. **Take the Square Root**:
- Now, take the square root to find \( V_c \):
\[ V_c = \sqrt{900} = 30 \, V \]

### Final Answer:
The potential across the capacitance (Vc) is **30 V**.