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A 50 μF capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.

Asked in GUJCET 2021 · Reactance and frequency

• (1) 5.2 A
• (2) 2.5 A
• (3) 3.8 A
• (4) 2.1 A

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 5.2 A. Sanity check: X_C=1/(2π(60)(50×10⁻⁶))=53.1 Ω, and (110)/(53.1)=2.07 A.
• (2) 2.5 A is the current a 60 μF capacitor would draw (110×2π×60×60×10⁻⁶=2.49 A), as if the 60 of the frequency were also the capacitance. Here C=50 μF gives 2.07 A.
• (3) No single slip gives 3.8 A. Sanity check: I=Vω C=110×377×50×10⁻⁶=2.07 A.

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