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What is the impedance of a circuit with a 4Ω resistor in series with a 3Ω induct

Practice Questions

Q1
What is the impedance of a circuit with a 4Ω resistor in series with a 3Ω inductor at a frequency of 60Hz (assuming inductive reactance of 18Ω)?
  1. 7Ω
  2. 22Ω
  3. 15Ω
  4. 21Ω

Questions & Step-by-Step Solutions

What is the impedance of a circuit with a 4Ω resistor in series with a 3Ω inductor at a frequency of 60Hz (assuming inductive reactance of 18Ω)?
  • Step 1: Identify the resistance (R) of the resistor, which is 4Ω.
  • Step 2: Identify the inductive reactance (X) of the inductor, which is given as 18Ω.
  • Step 3: Write the formula for impedance (Z) in a series circuit: Z = R + jX.
  • Step 4: Substitute the values into the formula: Z = 4Ω + j18Ω.
  • Step 5: To find the magnitude of the impedance |Z|, use the formula |Z| = √(R^2 + X^2).
  • Step 6: Calculate R^2: 4^2 = 16.
  • Step 7: Calculate X^2: 18^2 = 324.
  • Step 8: Add R^2 and X^2: 16 + 324 = 340.
  • Step 9: Take the square root of the sum: √340.
  • Step 10: Calculate √340, which is approximately 18.44Ω.
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