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)

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Q: 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)

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

Steps: 8

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.