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In a series RLC circuit, if the total impedance is 50Ω, the resistance is 30Ω, w

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Question: In a series RLC circuit, if the total impedance is 50Ω, the resistance is 30Ω, what is the inductive reactance if the capacitive reactance is 20Ω? (2023)

Options:

  1. 10Ω
  2. 20Ω
  3. 30Ω
  4. 40Ω

Correct Answer: 10Ω

Exam Year: 2023

Solution: 

Using Z = √(R² + (XL - XC)²), we find XL = √(50² - 30²) + 20 = 10Ω.

In a series RLC circuit, if the total impedance is 50Ω, the resistance is 30Ω, w

Practice Questions

Q1
In a series RLC circuit, if the total impedance is 50Ω, the resistance is 30Ω, what is the inductive reactance if the capacitive reactance is 20Ω? (2023)
  1. 10Ω
  2. 20Ω
  3. 30Ω
  4. 40Ω

Questions & Step-by-Step Solutions

In a series RLC circuit, if the total impedance is 50Ω, the resistance is 30Ω, what is the inductive reactance if the capacitive reactance is 20Ω? (2023)
  • Step 1: Identify the given values. We have total impedance (Z) = 50Ω, resistance (R) = 30Ω, and capacitive reactance (XC) = 20Ω.
  • Step 2: Write down the formula for total impedance in a series RLC circuit: Z = √(R² + (XL - XC)²).
  • Step 3: Substitute the known values into the formula: 50 = √(30² + (XL - 20)²).
  • Step 4: Calculate 30², which is 900. So, we have: 50 = √(900 + (XL - 20)²).
  • Step 5: Square both sides to eliminate the square root: 50² = 900 + (XL - 20)², which gives us 2500 = 900 + (XL - 20)².
  • Step 6: Subtract 900 from both sides: 2500 - 900 = (XL - 20)², resulting in 1600 = (XL - 20)².
  • Step 7: Take the square root of both sides: √1600 = XL - 20, which gives us 40 = XL - 20.
  • Step 8: Add 20 to both sides to solve for XL: 40 + 20 = XL, resulting in XL = 60Ω.
  • Step 9: The inductive reactance (XL) is 60Ω.
  • Impedance in RLC Circuits – Understanding the relationship between resistance, inductive reactance, and capacitive reactance in a series RLC circuit.
  • Phasor Representation – Using phasor representation to analyze the total impedance in AC circuits.
  • Reactance Calculation – Calculating inductive and capacitive reactance and their impact on total impedance.
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