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What is the impedance of a circuit with a 6Ω resistor in series with a 4Ω induct

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Question: What is the impedance of a circuit with a 6Ω resistor in series with a 4Ω inductor at a frequency of 50Hz (assuming inductive reactance XL = 2πfL)?

Options:

  1. 6Ω
  2. 8Ω
  3. 10Ω
  4. 4Ω

Correct Answer: 8Ω

Solution: 

Impedance in series is Z = R + jXL. If XL = 2π(50)(L) = 4Ω, then Z = 6Ω + j4Ω. The magnitude is √(6² + 4²) = 7.21Ω.

What is the impedance of a circuit with a 6Ω resistor in series with a 4Ω induct

Practice Questions

Q1
What is the impedance of a circuit with a 6Ω resistor in series with a 4Ω inductor at a frequency of 50Hz (assuming inductive reactance XL = 2πfL)?
  1. 6Ω
  2. 8Ω
  3. 10Ω
  4. 4Ω

Questions & Step-by-Step Solutions

What is the impedance of a circuit with a 6Ω resistor in series with a 4Ω inductor at a frequency of 50Hz (assuming inductive reactance XL = 2πfL)?
  • Step 1: Identify the components in the circuit. We have a resistor (R) of 6Ω and an inductor (L) with an inductive reactance (XL).
  • Step 2: Use the formula for inductive reactance, which is XL = 2πfL. Here, f is the frequency (50Hz).
  • Step 3: We need to find the value of L (inductance) that gives us XL = 4Ω. Rearranging the formula, we have L = XL / (2πf).
  • Step 4: Substitute the values into the formula: L = 4Ω / (2π(50Hz)). Calculate L to find its value.
  • Step 5: Now, we can find the total impedance (Z) of the circuit. The formula for impedance in series is Z = R + jXL.
  • Step 6: Substitute R = 6Ω and XL = 4Ω into the impedance formula: Z = 6Ω + j4Ω.
  • Step 7: To find the magnitude of the impedance, use the formula |Z| = √(R² + XL²). Substitute R = 6Ω and XL = 4Ω.
  • Step 8: Calculate the magnitude: |Z| = √(6² + 4²) = √(36 + 16) = √52.
  • Step 9: Finally, calculate √52 to get the approximate value of the impedance, which is about 7.21Ω.
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