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A current of frequency (50)/π Hz is passing through an A.C. circuit having a series combination of resistance R = 100 Ω and inductor L = 1 H. The phase difference between voltage and current is ______.

Asked in GSEB Board March 2018 · Impedance and phase angle

• (1) 60°
• (2) 45°
• (3) 30°
• (4) 90°

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 60° here. Sanity check: 60° needs tan φ = √3, i.e. X_L = √3 R ≈ 173 Ω, but X_L = 100 Ω = R.
• (3) No single slip gives 30° here. Sanity check: 30° needs tan φ = 1/(√3), i.e. X_L ≈ 57.7 Ω, but X_L = R gives tan φ = 1.
• (4) Ignores the resistance and treats the circuit as a pure inductor. With R = 100 Ω in series the voltage leads by less than 90°.

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