Question

In an LCR circuit, the current and emf differ in phase by $\Phi$. The value of $\Phi$ is:

• A. $\Phi = \tan^{-1}\left[\frac{(X_L - X_C)}{R}\right]$
• B. $\Phi = \tan^{-1}\left[\frac{(X_L + X_C)}{R}\right]$
• C. $\Phi = \tan^{-1}\left[\frac{R}{(X_L - X_C)}\right]$
• D. $\Phi = \tan^{-1}\left[\frac{R}{(X_L + X_C)}\right]$

Hint:

XL = ωL, XC = 1/(ωC). If XL greater than XC, circuit is inductive and voltage leads current.

Answer 1

The Correct Option is A

For a series LCR circuit, the total impedance is
\[Z = \sqrt{R^2 + (X_L - X_C)^2},\]
and the phase angle \( \Phi \) (between voltage and current) satisfies
\[\tan \Phi = \frac{X_L - X_C}{R}.\]