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In an RLC circuit, if the resistance is 6Ω, inductive reactance is 8Ω, and capac

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Question: In an RLC circuit, if the resistance is 6Ω, inductive reactance is 8Ω, and capacitive reactance is 4Ω, what is the total impedance? (2021)

Options:

  1. 10Ω
  2. 12Ω
  3. 14Ω
  4. 16Ω

Correct Answer: 12Ω

Exam Year: 2021

Solution: 

Total impedance Z = √(R² + (XL - XC)²) = √(6² + (8 - 4)²) = √(36 + 16) = √52 ≈ 10Ω.

In an RLC circuit, if the resistance is 6Ω, inductive reactance is 8Ω, and capac

Practice Questions

Q1
In an RLC circuit, if the resistance is 6Ω, inductive reactance is 8Ω, and capacitive reactance is 4Ω, what is the total impedance? (2021)
  1. 10Ω
  2. 12Ω
  3. 14Ω
  4. 16Ω

Questions & Step-by-Step Solutions

In an RLC circuit, if the resistance is 6Ω, inductive reactance is 8Ω, and capacitive reactance is 4Ω, what is the total impedance? (2021)
  • Step 1: Identify the values given in the problem. We have resistance (R) = 6Ω, inductive reactance (XL) = 8Ω, and capacitive reactance (XC) = 4Ω.
  • Step 2: Calculate the difference between inductive reactance and capacitive reactance. This is XL - XC = 8Ω - 4Ω = 4Ω.
  • Step 3: Square the resistance value. R² = 6² = 36.
  • Step 4: Square the result from Step 2. (XL - XC)² = 4² = 16.
  • Step 5: Add the results from Step 3 and Step 4. Total = R² + (XL - XC)² = 36 + 16 = 52.
  • Step 6: Take the square root of the total from Step 5 to find the total impedance. Z = √52.
  • Step 7: Calculate the square root of 52. Z ≈ 7.21Ω (approximately).
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