In a series LCR circuit, R = 30 Ω, X_L = 80 Ω, and X_C = 40 Ω. What is the total impedance Z of the circuit and the phase angle φ between the voltage and the current?

Answer and explanation

Correct answer: B. Z = 50 Ω, φ = tan⁻¹(4/3) with current lagging voltage

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  1. Step 1: In a series LCR circuit, total impedance is: .
  2. Step 2: Substitute , , and :
  3. Step 3: The phase angle is given by: , so .
  4. Step 4: Since , the circuit is predominantly inductive, meaning the voltage leads the current, or equivalently, the current lags behind the voltage.
Answer
Z = 50 Ω, φ = tan⁻¹(4/3) with current lagging voltage
Why not the others: 'Z = 150 Ω, φ = 0°' simply adds the impedances scalar-wise (); 'Z = 50 Ω, current leading voltage' incorrectly identifies the circuit as capacitive (leading current only occurs when ); 'Z = 70 Ω' computes ignoring quadrature addition.

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