Pure resistors — is the resistor’s voltage always out of phase with the current?
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ATrue
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BFalse
Answer
Correct Answer: False
Explanation
Introduction / Context:Phase relationships between voltage and current define how elements store or dissipate energy. This item checks the unique, purely dissipative behavior of an ideal resistor.
Given Data / Assumptions:
- Ideal resistor R only; no reactive components.
- Sinusoidal steady-state excitation.
Concept / Approach:In a pure resistor, voltage and current are in phase. Inductors and capacitors cause phase shifts of +90 degrees (current lags) and −90 degrees (current leads), respectively; resistors cause none.
Step-by-Step Solution:
Ohm’s law in phasor form: V = I * R (R is real).Phasor angle of R is 0 degrees, so angle(V) − angle(I) = 0.Therefore, v(t) and i(t) reach maxima and zeros simultaneously—no phase difference.Verification / Alternative check:Instantaneous power p(t) = v(t) * i(t) is always non-negative for a resistor, consistent with no reactive energy exchange and reinforcing zero phase shift.
Why Other Options Are Wrong:
- Selecting “True” confuses resistors with reactive elements that store energy and introduce phase shifts.
Common Pitfalls:Assuming some phase difference must exist because AC is involved. AC does not guarantee phase shifts; it depends on element type.
Final Answer:False