*Question E5B11:
What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 25 ohms, R is 100 ohms, and XL is 75 ohms?*  

*Correct Answer is  B: 27 degrees with the voltage leading the current*  

### AI Response: (may contain errors)  

To determine the phase angle between the voltage and the current in a series RLC circuit, we need to calculate the net reactance and then use it to find the phase angle.

### Step-by-step Explanation:

1. **Calculate Net Reactance ($X$):**

   The net reactance in a series RLC circuit is given by the difference between the inductive reactance ($X_L$) and the capacitive reactance ($X_C$):

   $$X = X_L - X_C$$

   Given:
   - $X_C = 25 \, \text{ohms}$
   - $X_L = 75 \, \text{ohms}$

   Substitute the values:

   $$X = 75 \, \text{ohms} - 25 \, \text{ohms} = 50 \, \text{ohms}$$

2. **Calculate the Phase Angle ($\theta$):**

   The phase angle $\theta$ in a series RLC circuit is determined by the arctangent of the net reactance divided by the resistance ($R$):

   $$\theta = \arctan\left(\frac{X}{R}\right)$$

   Given:
   - $R = 100 \, \text{ohms}$

   Substitute the values:

   $$\theta = \arctan\left(\frac{50}{100}\right) = \arctan(0.5)$$

   Using a calculator, $\arctan(0.5) \approx 26.57$ degrees, which we round to 27 degrees.

3. **Determine the Direction of the Phase Angle:**

   - Since $X_L > X_C$, the net reactance is inductive, meaning the voltage leads the current in an inductive circuit.

### Conclusion:

- **Correct Answer: B: 27 degrees with the voltage leading the current**

### Why Other Choices Are Incorrect:

- **A: 27 degrees with the voltage lagging the current**: Incorrect because the net reactance is inductive, not capacitive, so the voltage leads, not lags.
- **C: 63 degrees with the voltage lagging the current**: Incorrect because the calculated phase angle is 27 degrees, not 63 degrees, and the voltage leads, not lags.
- **D: 63 degrees with the voltage leading the current**: Incorrect because the calculated phase angle is 27 degrees, not 63 degrees.

This explanation shows how to calculate the phase angle and determine the relationship between voltage and current in a series RLC circuit.