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A pure inductor of 50.0 mH is connected to a source of 220 V. Then rms current in the circuit will be _________. The frequency of the source is 50 Hz.

Asked in GUJCET 2024 · Reactance and frequency

• (1) 7 A
• (2) 28 A
• (3) 14 A
• (4) 21 A

Step-by-step solution

Why the other options are wrong

• (1) 7 A would need a reactance of (220)/7=31.4 Ω, exactly twice the true X_L, and nothing in X_L=2π fL doubles here. Sanity check: 2π(50)(0.050)=15.7 Ω, so Iᵣₘₛ=(220)/(15.7)=14 A.
• (2) Comes from dropping the 2 in ω=2π f: X_L=π(50)(0.050)=7.85 Ω halves the reactance, so the current doubles to (220)/(7.85)=28 A.
• (4) No slip produces 21 A: it would need X_L=(220)/(21)=10.5 Ω, which 2π fL cannot give with these numbers — the four options are simply multiples of 7 A set around the answer. Sanity check: X_L=15.7 Ω gives 14 A.

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