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A circuit has a resistance of 10Ω and a reactance of 5Ω. What is the impedance o

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Question: A circuit has a resistance of 10Ω and a reactance of 5Ω. What is the impedance of the circuit? (2021)

Options:

  1. 5Ω
  2. 10Ω
  3. √125Ω
  4. √(10² + 5²)Ω

Correct Answer: √(10² + 5²)Ω

Exam Year: 2021

Solution: 

The impedance Z is calculated as Z = √(R² + X²) = √(10² + 5²) = √125Ω.

A circuit has a resistance of 10Ω and a reactance of 5Ω. What is the impedance o

Practice Questions

Q1
A circuit has a resistance of 10Ω and a reactance of 5Ω. What is the impedance of the circuit? (2021)
  1. 5Ω
  2. 10Ω
  3. √125Ω
  4. √(10² + 5²)Ω

Questions & Step-by-Step Solutions

A circuit has a resistance of 10Ω and a reactance of 5Ω. What is the impedance of the circuit? (2021)
  • Step 1: Identify the resistance (R) and reactance (X) values from the problem. Here, R = 10Ω and X = 5Ω.
  • Step 2: Use the formula for impedance (Z), which is Z = √(R² + X²).
  • Step 3: Calculate R². This is 10² = 100.
  • Step 4: Calculate X². This is 5² = 25.
  • Step 5: Add R² and X² together. This is 100 + 25 = 125.
  • Step 6: Take the square root of the sum. This is √125.
  • Step 7: Simplify √125. This is approximately 11.18Ω.
  • Impedance Calculation – Impedance in an AC circuit is calculated using the formula Z = √(R² + X²), where R is resistance and X is reactance.
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