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?  

Choices:  
A: 27 degrees with the voltage lagging the current  
B: 27 degrees with the voltage leading the current  
C: 63 degrees with the voltage lagging the current  
D: 63 degrees with the voltage leading the current    

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

To find the phase angle in a series RLC circuit:

- Net reactance:  
  $$X = X_L - X_C = 75 - 25 = +50\ \Omega \quad (\text{inductive})$$
- Phase angle (angle of impedance):  
  $$\phi = \tan^{-1}\left(\frac{X}{R}\right) = \tan^{-1}\left(\frac{50}{100}\right) = \tan^{-1}(0.5) \approx 26.6^\circ \approx 27^\circ$$
- Sign/direction: Inductive net reactance means current lags voltage, so voltage leads current.

Therefore, the correct answer is: 27 degrees with the voltage leading the current (Choice B).

Why the other choices are incorrect:
- A: 27 degrees lagging would be for a capacitive circuit (if $X_C > X_L$). Here it’s inductive.
- C: 63 degrees lagging is wrong magnitude and wrong direction. 63° would require $|X|/R \approx 2$, not 0.5.
- D: 63 degrees leading has the correct direction for inductive, but the angle is too large; our ratio gives about 27°, not 63°.

Useful formulas and rules:
- Series RLC impedance:  
  $$Z = R + j(X_L - X_C)$$
- Phase angle (voltage relative to current):  
  $$\phi = \tan^{-1}\left(\frac{X_L - X_C}{R}\right)$$
  - $\phi > 0$ (inductive): voltage leads current.
  - $\phi < 0$ (capacitive): voltage lags current.
- Mnemonic: “ELI the ICE man” — in an inductor, voltage (E) leads current (I); in a capacitor, current (I) leads voltage (E).