In an RC series circuit connected across and AC source of 150 V 70 Hz, the value of R is 820 `Omega` and voltage across it is 100V. Calculate the voltage drop across capacitor connected in series.

Answer

To solve the problem of finding the voltage drop across the capacitor in an RC series circuit connected to an AC source, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Total voltage across the circuit (V) = 150 V
- Voltage across the resistor (Vr) = 100 V
- Resistance (R) = 820 Ω
- Frequency (f) = 70 Hz (not needed for this calculation)

2. **Understand the Relationship**:
In an RC series circuit, the voltages across the resistor (Vr) and the capacitor (Vc) are perpendicular to each other. Therefore, we can use the Pythagorean theorem to relate these voltages to the total voltage (V):
\[ V^2 = Vr^2 + Vc^2 \]

3. **Rearrange the Equation**:
To find the voltage across the capacitor (Vc), we can rearrange the equation:
\[ Vc^2 = V^2 - Vr^2 \]

4. **Substitute Known Values**:
Substitute the known values into the equation:
\[ Vc^2 = 150^2 - 100^2 \]

5. **Calculate the Squares**:
Calculate \(150^2\) and \(100^2\):
\[ 150^2 = 22500 \]
\[ 100^2 = 10000 \]

6. **Subtract the Squares**:
Now, subtract the square of the voltage across the resistor from the square of the total voltage:
\[ Vc^2 = 22500 - 10000 = 12500 \]

7. **Take the Square Root**:
Finally, take the square root to find Vc:
\[ Vc = \sqrt{12500} \approx 111.8 \, V \]

### Final Answer:
The voltage drop across the capacitor is approximately **111.8 V**.

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