Frequency effect in series RL: When the frequency of the applied AC voltage is decreased, what happens to the total impedance magnitude of a series RL circuit?

Introduction / Context:This item tests understanding that the inductive reactance in a series RL circuit depends on frequency, directly influencing total impedance.

Given Data / Assumptions:

• Series RL with fixed R and L.
• AC steady state, frequency f changes.

Concept / Approach:Impedance magnitude is Z = sqrt(R^2 + XL^2). Since XL = 2 * pi * f * L, reducing f reduces XL, thereby reducing the vector sum unless R completely dominates already (in which case Z tends toward R). In all cases with finite L, lowering f cannot increase XL, so Z does not increase.

Step-by-Step Solution:

Verification / Alternative check:Limits: as f → 0, XL → 0 and Z → R. As f → ∞, Z → ∞ (inductor dominating). The trend with decreasing f is consistent: Z goes down.

Why Other Options Are Wrong:

• 'increases': Opposite of XL behavior.
• 'does not change': Would require L = 0 (no inductor), contrary to setup.
• 'cannot be determined': Determinable from formula.

Common Pitfalls:

• Confusing series with parallel RL behavior.

Final Answer:decreases