Question

For a series LCR circuit, what is the formula for the phase angle between current and emf?

• A. $\tan \phi = \frac{X_L - X_C}{R}$
• B. $\tan \phi = \frac{R}{X_L - X_C}$
• C. $\sin \phi = \frac{X_L - X_C}{R}$
• D. $\cos \phi = \frac{X_L - X_C}{R}$

Hint:

Remember: $\tan \phi = \frac{\text{Reactance}}{\text{Resistance}}$.

Answer 1

The Correct Option is A

Concept: In a series LCR circuit, the phase difference between current and applied emf depends on resistance and reactance.
Step 1: Understanding reactance.
Inductive reactance: $X_L = \omega L$
Capacitive reactance: $X_C = \frac{1}{\omega C}$
Step 2: Net reactance.
\[ X = X_L - X_C \]
Step 3: Phase angle formula.
\[ \tan \phi = \frac{X}{R} = \frac{X_L - X_C}{R} \]
Step 4: Evaluating the options.

• $\tan \phi = \frac{X_L - X_C}{R}$ $\rightarrow$ Correct
• $\tan \phi = \frac{R}{X_L - X_C}$ $\rightarrow$ Incorrect
• $\sin \phi = \frac{X_L - X_C}{R}$ $\rightarrow$ Incorrect
• $\cos \phi = \frac{X_L - X_C}{R}$ $\rightarrow$ Incorrect

Step 5: Conclusion.
Thus, the phase angle is given by $\tan \phi = \frac{X_L - X_C}{R}$.