Question

In AC circuits, the relation that holds is \( Z = \frac{E_U}{I_U} \), where:

• A. \( Z = \sqrt{R^2 + X_L^2} \) in case of a.c. circuit containing R and L in series
• B. \( Z = \sqrt{R^2 + X_C^2} \) in case of a.c. circuit containing R and C in series
• C. \( Z = X_L - X_C \) in case of a.c. circuit containing L and C in series
• D. \( Z = \sqrt{R^2 + (X_L - X_C)^2} \) in case of a.c. circuit containing R, L, and C in series

Hint:

Impedance is calculated by considering the resistive, inductive, and capacitive components of the circuit, following the given formulas based on the arrangement.

Answer 1

The Correct Option is B

In AC circuits, the impedance \(Z\) is calculated depending on whether the components are resistors, inductors, or capacitors: - For a circuit containing a resistor and an inductor in series, the impedance is: \[ Z = \sqrt{R^2 + X_L^2} \] - For a circuit containing a resistor and a capacitor in series, the impedance is: \[ Z = \sqrt{R^2 + X_C^2} \] - For a circuit containing only an inductor and a capacitor in series, the impedance is: \[ Z = |X_L - X_C| \] Thus, the correct answer is A, B, and C only.