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A resistor of 10 Ω and a capacitor of 100 μF are connected in series to an AC so

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Question: A resistor of 10 Ω and a capacitor of 100 μF are connected in series to an AC source of frequency 50 Hz. What is the capacitive reactance? (2020)

Options:

  1. 3.18 Ω
  2. 31.8 Ω
  3. 0.318 Ω
  4. 318 Ω

Correct Answer: 3.18 Ω

Exam Year: 2020

Solution: 

Capacitive reactance Xc = 1/(2πfC) = 1/(2π(50)(100 × 10^-6)) ≈ 3.18 Ω.

A resistor of 10 Ω and a capacitor of 100 μF are connected in series to an AC so

Practice Questions

Q1
A resistor of 10 Ω and a capacitor of 100 μF are connected in series to an AC source of frequency 50 Hz. What is the capacitive reactance? (2020)
  1. 3.18 Ω
  2. 31.8 Ω
  3. 0.318 Ω
  4. 318 Ω

Questions & Step-by-Step Solutions

A resistor of 10 Ω and a capacitor of 100 μF are connected in series to an AC source of frequency 50 Hz. What is the capacitive reactance? (2020)
  • Step 1: Identify the values given in the problem. We have a frequency (f) of 50 Hz and a capacitance (C) of 100 μF.
  • Step 2: Convert the capacitance from microfarads to farads. 100 μF is equal to 100 × 10^-6 F.
  • Step 3: Write down the formula for capacitive reactance (Xc): Xc = 1 / (2πfC).
  • Step 4: Substitute the values into the formula. Replace f with 50 and C with 100 × 10^-6.
  • Step 5: Calculate the denominator: 2π(50)(100 × 10^-6).
  • Step 6: Perform the multiplication: 2π(50) = 100π and then multiply by (100 × 10^-6).
  • Step 7: Calculate the total value in the denominator.
  • Step 8: Take the reciprocal of the result from Step 7 to find Xc.
  • Capacitive Reactance – Capacitive reactance (Xc) is the opposition that a capacitor offers to the flow of alternating current (AC), calculated using the formula Xc = 1/(2πfC), where f is the frequency and C is the capacitance.
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