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In an RLC circuit, if the resistance is 10Ω, the inductance is 0.1H, and the cap

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Question: In an RLC circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 20μF, what is the total impedance at 50Hz? (2022)

Options:

  1. 10Ω
  2. 15.81Ω
  3. 20Ω
  4. 25Ω

Correct Answer: 15.81Ω

Exam Year: 2022

Solution: 

Calculate XL = 2πfL = 31.42Ω and XC = 1/(2πfC) = 159.15Ω. Z = √(R² + (XL - XC)²) = √(10² + (31.42 - 159.15)²) = 15.81Ω.

In an RLC circuit, if the resistance is 10Ω, the inductance is 0.1H, and the cap

Practice Questions

Q1
In an RLC circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 20μF, what is the total impedance at 50Hz? (2022)
  1. 10Ω
  2. 15.81Ω
  3. 20Ω
  4. 25Ω

Questions & Step-by-Step Solutions

In an RLC circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 20μF, what is the total impedance at 50Hz? (2022)
  • Step 1: Identify the given values: Resistance (R) = 10Ω, Inductance (L) = 0.1H, Capacitance (C) = 20μF, Frequency (f) = 50Hz.
  • Step 2: Convert capacitance from microfarads to farads: 20μF = 20 x 10^-6 F = 0.00002 F.
  • Step 3: Calculate the inductive reactance (XL) using the formula: XL = 2πfL.
  • Step 4: Substitute the values into the formula: XL = 2π(50)(0.1) = 31.42Ω.
  • Step 5: Calculate the capacitive reactance (XC) using the formula: XC = 1/(2πfC).
  • Step 6: Substitute the values into the formula: XC = 1/(2π(50)(0.00002)) = 159.15Ω.
  • Step 7: Calculate the total impedance (Z) using the formula: Z = √(R² + (XL - XC)²).
  • Step 8: Substitute the values into the formula: Z = √(10² + (31.42 - 159.15)²).
  • Step 9: Calculate the difference: XL - XC = 31.42 - 159.15 = -127.73.
  • Step 10: Square the difference: (-127.73)² = 16319.52.
  • Step 11: Calculate R²: 10² = 100.
  • Step 12: Add R² and the squared difference: 100 + 16319.52 = 16419.52.
  • Step 13: Take the square root to find Z: Z = √(16419.52) = 128.14Ω.
  • Impedance in RLC Circuits – Understanding how to calculate the total impedance in a circuit with resistance, inductance, and capacitance.
  • Reactance Calculation – Calculating inductive reactance (XL) and capacitive reactance (XC) using frequency, inductance, and capacitance.
  • Phasor Relationships – Applying the Pythagorean theorem to find the total impedance from resistance and the difference between reactances.
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