Question

Differentiate between inductive reactance, capacitive reactance and impedance of an ac circuit.
An ideal inductor and an ideal capacitor are connected in series across an ac voltage. Plot a graph showing variation of net reactance of the circuit with frequency of the applied ac voltage.

Hint:

In a pure LC circuit, at resonance, the impedance becomes zero, ideally leading to infinite current.

Answer 1

Step 1: Understanding the Concept:
Reactance and impedance represent the opposition offered by components to the flow of alternating current. Reactance depends on frequency, while impedance is the total effective opposition of the circuit.

Step 2: Detailed Explanation:
(a) Differentiation:

Inductive Reactance (\(X_L\)): Opposition by an inductor. \(X_L = \omega L = 2\pi f L\). It increases with frequency.
Capacitive Reactance (\(X_C\)): Opposition by a capacitor. \(X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}\). It decreases with frequency.
Impedance (\(Z\)): The total opposition offered by a combination of \(R, L,\) and \(C\). \(Z = \sqrt{R^2 + (X_L - X_C)^2}\).
(b) Net Reactance Graph: For a series LC circuit, net reactance \(X = |X_L - X_C|\). At resonance frequency \(f_r\), \(X_L = X_C\) and net reactance is zero. Below \(f_r\), it is capacitive; above \(f_r\), it is inductive.

Step 3: Final Answer:
Inductive reactance is \(2\pi f L\), capacitive is \(1/(2\pi f C)\), and impedance is the vector sum of resistance and total reactance.