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A circuit has a resistance of 10 Ω and a reactance of 10 Ω. What is the impedanc

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Question: A circuit has a resistance of 10 Ω and a reactance of 10 Ω. What is the impedance of the circuit? (2020)

Options:

  1. 10 Ω
  2. 14.14 Ω
  3. 20 Ω
  4. 5 Ω

Correct Answer: 14.14 Ω

Exam Year: 2020

Solution: 

The impedance Z = √(R² + X²) = √(10² + 10²) = √200 = 14.14 Ω.

A circuit has a resistance of 10 Ω and a reactance of 10 Ω. What is the impedanc

Practice Questions

Q1
A circuit has a resistance of 10 Ω and a reactance of 10 Ω. What is the impedance of the circuit? (2020)
  1. 10 Ω
  2. 14.14 Ω
  3. 20 Ω
  4. 5 Ω

Questions & Step-by-Step Solutions

A circuit has a resistance of 10 Ω and a reactance of 10 Ω. What is the impedance of the circuit? (2020)
  • Step 1: Identify the resistance (R) and reactance (X) values. Here, R = 10 Ω and X = 10 Ω.
  • Step 2: Use the formula for impedance (Z), which is Z = √(R² + X²).
  • Step 3: Calculate R². Since R = 10 Ω, R² = 10² = 100.
  • Step 4: Calculate X². Since X = 10 Ω, X² = 10² = 100.
  • Step 5: Add R² and X² together. So, 100 + 100 = 200.
  • Step 6: Take the square root of the sum. √200 = 14.14.
  • Step 7: The impedance of the circuit is 14.14 Ω.
  • Impedance Calculation – Understanding how to calculate the impedance of a circuit using resistance and reactance.
  • Complex Numbers in AC Circuits – Recognizing that impedance is a complex quantity that combines resistance and reactance.
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