*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 find the phase angle between the voltage across and the current through a series RLC circuit, we can use the following relationships:

1. **Impedance Calculation**: The total impedance $Z$ in a series RLC circuit is given by:

   $$Z = R + j(X_L - X_C)$$

   where:
   - $R$ = resistance (100 ohms)
   - $X_L$ = inductive reactance (75 ohms)
   - $X_C$ = capacitive reactance (25 ohms)

2. **Phase Angle Calculation**: The phase angle $\phi$ can be calculated using:

   $$\tan(\phi) = \frac{X_L - X_C}{R}$$

   Substituting the values:

   $$\tan(\phi) = \frac{75 - 25}{100} = \frac{50}{100} = 0.5$$

   To find the phase angle $\phi$, we take the arctangent:

   $$\phi = \tan^{-1}(0.5)$$

   This gives us:

   $$\phi \approx 26.57^\circ$$

   Rounding this, we find that $\phi \approx 27^\circ$.

3. **Leading or Lagging**: In a series RLC circuit:
   - If $X_L > X_C$, the circuit is inductive, and the voltage leads the current.
   - If $X_C > X_L$, the circuit is capacitive, and the voltage lags the current.

   Since $X_L (75 \, \text{ohms}) > X_C (25 \, \text{ohms})$, the voltage leads the current.

### Summary of Choices:
- **Correct Answer**: 
  - **A**: 27 degrees with the voltage lagging the current (Incorrect)
  - **B**: 27 degrees with the voltage leading the current (Correct)
  - **C**: 63 degrees with the voltage lagging the current (Incorrect)
  - **D**: 63 degrees with the voltage leading the current (Incorrect)

### Why Other Choices are Incorrect:
- **Choice A**: Incorrect because the voltage does not lag; it leads.
- **Choice C**: Incorrect because the calculated angle is approximately 27 degrees, not 63 degrees.
- **Choice D**: Incorrect for the same reason as C; the angle is not 63 degrees, and the voltage leads, not lags.

### Key Takeaway:
- The phase angle in a series RLC circuit can be determined using the impedance and the relationship between inductive and capacitive reactance. In this case, the voltage leads the current by approximately 27 degrees.