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A pure inductor of 25.48 mH and a pure resistor of 8 Ω are connected in series with an A.C. source of frequency 50 Hz. The phase difference between the current (I) and the voltage (V) in this circuit is _____________.

Asked in GUJCET 2023 · Impedance and phase angle

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

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives 30°. Sanity check: X_L=2π(50)(25.48×10⁻³)=8.0 Ω=R, so tan φ=1 and φ=45°.
• (3) 60° comes from adding R and X_L as plain numbers: Z=8+8=16 Ω and cos φ=8/(16)=1/2. They add in quadrature: Z=√8²+8²=11.3 Ω.
• (4) 90° is a pure inductor on its own. The 8 Ω resistor in series pulls the phase difference below 90°.

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