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Circuit and electromagnetism basics

What is the magnitude of the impedance of a circuit with a resistor R = 30 Ω in series with a coil of reactance XL = 40 Ω? (Ignore the coil's resistance.)

  1. A70 Ω
  2. B10 Ω
  3. C50 Ω
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Answer: C. 50 Ω

The voltages across a resistor and an inductor are 90° out of phase, so they are combined as complex numbers (vectors), not added directly. Z = R + jXL = 30 + j40 Ω, with magnitude √(30² + 40²) = √2500 = 50 Ω. The current lags the voltage by φ = tan⁻¹(40/30) ≈ 53°, and the power factor is cos φ = 30/50 = 0.6.

  • A. 70 Ω simply adds the two, ignoring the phase difference.
  • B. 10 Ω takes the difference, which is the wrong way to combine them.
  • C. Correct. √(30² + 40²) = 50 Ω.
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