Question

Given below are two statements:
Statement-I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.
Statement-II : In ac circuit, the average power delivered by the source never becomes zero.
In the light of the above statements, choose the correct answer from the options given below.

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Answer 1

The Correct Option is C

 The problem involves two statements regarding AC circuits and their characteristics.

1. Statement I: "The reactance of an AC circuit is zero. It is possible that the circuit contains a capacitor and an inductor."
2. Statement II: "In an AC circuit, the average power delivered by the source never becomes zero."

Let's evaluate each statement individually:

1. Analysis of Statement I:
   • The reactance in an AC circuit can be written as \(X = X_L - X_C\), where \(X_L\) is the inductive reactance and \(X_C\) is the capacitive reactance.
   • If the reactance of the circuit is zero, i.e., \(X = 0\), this implies \(X_L = X_C\).
   • This condition can occur in a series RLC circuit when the circuit is at resonance, given that the frequency is such that the inductive reactance and capacitive reactance are equal.
   • Thus, Statement I is true since a circuit can indeed contain both a capacitor and an inductor, resulting in zero total reactance at resonance.
2. Analysis of Statement II:
   • The average power delivered in an AC circuit is given by \(P = VI\cos(\phi)\), where \(\cos(\phi)\) is the power factor of the circuit.
   • For purely reactive loads, like purely inductive or capacitive (e.g., where \(\phi = 90^\circ\) or \(\phi = -90^\circ\)), the power factor \(\cos(\phi) = 0\), making the average power delivered \(P = 0\).
   • Thus, the statement that the average power delivered never becomes zero is false for circuits that are purely reactive.

Based on the analysis:

• Statement I is true as it is possible for both a capacitor and an inductor to exist in the circuit, counterbalancing each other's reactance.
• Statement II is false because in special conditions (purely reactive circuits), the average power can indeed become zero.

Therefore, the correct answer is: Statement I is true but Statement II is false.