For RL series circuit, impedance is given by

<p>Z²=R²+X_L²</p>

{"type":"technical","methodBadge":"Concept & Principle","explanation":"The correct impedance for an RL series circuit is given by the formula $Z = \\sqrt{R^2 + X_L^2}$, where $Z$ is the impedance, $R$ is the resistance, and $X_L$ is the inductive reactance. This equation illustrates how resistance and inductive reactance contribute to the overall impedance in an alternating current circuit.","workingPrinciple":"The impedance in an RL circuit arises due to both the resistance and the inductive reactance, which is a measure of how much the inductor opposes the change in current. The combined effect leads to a complex impedance that determines how the circuit will respond to alternating current.","keyFormulas":["$Z = \\sqrt{R^2 + X_L^2}$ — Impedance of an RL circuit",null],"keyPoints":["Impedance encompasses both resistance and reactance in AC circuits.","The inductive reactance is proportional to the frequency and inductance: $X_L = 2\\pi f L$."],"advantages":["Allows for understanding of circuit behavior in AC systems","Essential for designing circuits with inductors"],"disadvantages":["Complex calculations can be necessary for multiple components","Phase differences must be considered for accurate analysis"],"applications":["Used in power transmission lines","Essential for designing filters and oscillators"],"comparisonTable":[],"additionalInfo":[{"parameter":"Standard Values","detail":"Common values for inductors vary based on application and frequency used."},{"parameter":"Wrong Options Explained","detail":"Option B is incorrect as it refers to capacitive reactance; Option C misrepresents impedance as purely resistive."}],"answer":"A is correct — the formula accurately represents the impedance in an RL circuit.","coreConcepts":["Impedance in AC circuits","Resistance and reactance","Inductive reactance"],"crossTopicTip":"Understanding impedance is crucial not only in electrical engineering but also in applications involving waves and signal processing."}