Parallel RL network phase angle: A 100 Ω resistor is connected in parallel with an inductor whose reactance magnitude is 200 Ω at the operating frequency. What is the phase shift between the total current and the applied voltage?

Introduction / Context:
In a parallel RL circuit, the resistive branch current is in phase with the voltage, while the inductive branch current lags the voltage by 90 degrees. The total current is the phasor sum of these two components. The question asks for the overall phase angle between the total current and the applied voltage.

Given Data / Assumptions:

• Resistor R = 100 Ω.
• Inductive reactance magnitude X_L = 200 Ω.
• Ideal components; sinusoidal steady state.
• Voltage is the reference phasor.

Concept / Approach:
Use admittance to combine parallel branches: Y_total = G + jB. For a resistor, G = 1 / R. For an inductor, susceptance B_L = −1 / X_L (negative because current lags). The total current I_total = V * Y_total; the angle of I_total relative to V is φ = arctan(B / G). A negative φ means the current lags the voltage.

Step-by-Step Solution:
Compute conductance: G = 1 / R = 1 / 100 = 0.01 S.Compute susceptance: B = −1 / X_L = −1 / 200 = −0.005 S.Find angle: φ = arctan(B / G) = arctan(−0.005 / 0.01) = arctan(−0.5).Evaluate: arctan(−0.5) ≈ −26.6 degrees ⇒ current lags voltage by 26.6 degrees.

Verification / Alternative check:
Phasor diagram: the in-phase component equals I_R = V / R; the quadrature lagging component equals I_L = V / X_L. The tangent of the lag angle is I_L / I_R = (V / X_L) / (V / R) = R / X_L = 100 / 200 = 0.5, matching arctan(0.5) = 26.6 degrees.

Why Other Options Are Wrong:
0 degree: only for purely resistive or perfectly balanced susceptance to zero.90 degree or 180 degree: would require pure reactance or phase inversion; not applicable here.None of the above: incorrect because 26.6 degree is correct.

Common Pitfalls:
Using impedance instead of admittance for parallel combination; forgetting the negative sign for inductive susceptance; mixing degrees and radians.

Final Answer:
26.6 degree