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?
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Adecreases
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Bincreases
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Cdoes not change
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Dcannot be determined without values
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Ebecomes purely resistive and infinite
Answer
Correct Answer: decreases
Explanation
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:
XL = 2 * pi * f * L.Decrease f ⇒ decrease XL.Z = sqrt(R^2 + XL^2) shrinks toward R as XL decreases.Therefore, the impedance magnitude decreases.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