NEETPhysicsAlternating Current
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In a series LCR circuit with L = 0.1 H and C = 10 F connected to an AC source V = 200 (1000t) , the power factor is unity. Reason (R): The linear frequency ( ) of the AC source is 1000 Hz , which is equal to the resonant frequency ( ₀ ) of the circuit. In the light of the above statements, choose t
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A).
- B(A) is true but (R) is false.
- CBoth (A) and (R) are true but (R) is not the correct explanation of (A).
- D(A) is false but (R) is true.
Correct answer
B. (A) is true but (R) is false.
Step-by-step solution
For the given AC source V = 200 (1000t) , the angular frequency is = 1000 rad s ⁻¹ . The resonant angular frequency of the circuit is: ₀ = 1 LC = 1 0.1 10 10⁻⁶ = 1000 rad s ⁻¹ Since = ₀ , the circuit is at resonance and the power factor is unity ( = 1 ). Thus, Assertion (A) is true. The linear frequency of the source is = 2 = 1000 2 = 500 Hz . The value 1000 refers to the angular frequency, not the linear frequency. Thus, Reason (R) is false. Answer: (A) is true but (R) is false.