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A 15 μF capacitor is connected to a 220 V, 50 Hz a.c. source. The value of the capacitive reactance is ______.

Asked in GSEB Board March 2020 · Reactance and frequency

• (1) 424 Ω
• (2) 106 Ω
• (3) 212 Ω
• (4) 21.2 Ω

Step-by-step solution

Why the other options are wrong

• (1) Drops the 2 in 2π f: 1/(π fC)=1/(π×50×15×10⁻⁶)=424 Ω, twice the true value.
• (2) Comes from using 100 Hz, the number of times a 50 Hz current reverses each second, in place of the frequency: 1/(2π×100×15×10⁻⁶)=106 Ω.
• (4) A power-of-ten slip in the capacitance: taking 15 μF as 15×10⁻⁵ F gives 21.2 Ω. One microfarad is 10⁻⁶ F.

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