Core AC/DC concepts — units check: Which SI unit is used to measure resistance, reactance, and impedance in electrical circuits?

Question

Accepted Answer

Introduction / Context: Knowing the correct SI units anchors understanding of circuit quantities and avoids dimensionally inconsistent calculations. Resistance (DC opposition), reactance (AC frequency-dependent opposition), and impedance (general complex opposition) are all measures of how much a circuit resists current flow. Given Data / Assumptions: We must identify a single unit that applies to resistance (R), reactance (X), and impedance (Z). Recall common SI units: ohm (Ω), farad (F), henry (H), watt (W), siemens (S). Context includes both DC and AC circuits. Concept / Approach: Resistance, reactance, and impedance are all quantities of electrical opposition with the same dimension of volts per ampere. Volts per ampere defines the ohm. In AC, reactance X and impedance Z are often represented as frequency-dependent or complex values, but their magnitude is still in ohms. Siemens is the reciprocal unit (conductance, admittance, susceptance). Step-by-Step Solution: Map quantities to units: R → ohms, X → ohms, Z → ohms.Confirm dimensional analysis: 1 Ω = 1 V / 1 A.Exclude unrelated units: F for capacitance, H for inductance, W for power, S for conductance.Choose the common unit: ohm. Verification / Alternative check: Ohm’s law in DC: V = I * R (R in ohms). In AC phasors: Ṽ = Ĩ * Z̃ (Z in ohms). Reactance formulas X_L = 2 * π * f * L and X_C = 1 / (2 * π * f * C) both produce ohms, confirming consistency. Why Other Options Are Wrong: Farad measures capacitance, henry measures inductance, watt measures power, siemens measures conductance (the inverse of ohms). Common Pitfalls: Confusing admittance (S) with impedance (Ω), and forgetting that even though impedance can be complex, its unit is still the ohm. Final Answer: ohm

Quantities and Units Questions