COMEDK · Physics · 23. Alternating Current

In an electrical circuit \(R, L, C\) and \(\mathrm{AC}\) voltage source are all connected in series. When \(L\) is removed from the circuit, the phase difference between the voltage and the current in the circuit is \(\pi / 3\). If instead \(C\) is removed from the circuit, the phase difference is again \(\pi / 3\). The power factor of the circuit is

A \(\dfrac{\sqrt{3}}{2}\)
B \(1 / 2\)
C 1
D \(1 \sqrt{2}\)

Verified Solution

Answer & Solution

Correct Answer

(C) 1

Step-by-step Solution

Detailed explanation

In an \(LCR\) series circuit, the phase difference \(\phi\) is given by \(\tan \phi = \dfrac{X_L - X_C}{R}\). When \(L\) is removed, the circuit contains only \(R\) and \(C\). The phase difference is \(\phi_1 = -\pi / 3\). Thus, \(\tan(-\pi / 3) = \dfrac{-X_C}{R}\), which…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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