Power factor is calculated by

$R/Z$

{"type":"technical","methodBadge":"Concept & Principle","explanation":"The power factor of an A.C. circuit is defined as the cosine of the phase angle difference between the voltage and current. In a series RLC circuit, it represents the ratio of the real power (resistance) to the apparent power (impedance).","workingPrinciple":"In an A.C. series circuit, the total impedance $Z$ is the vector sum of resistance $R$ and reactance $X$. The voltage leads or lags the current by an angle $\\phi$. Since $R$ is the base component of the impedance triangle and $Z$ is the hypotenuse, the power factor is given by the ratio $\\frac{R}{Z}$, which corresponds to $\\cos(\\phi)$.","diagramSvg":"RXZ\\phi","keyFormulas":["$PF = \\cos(\\phi) = \\frac{R}{Z}$ — Power factor in terms of resistance and impedance","$Z = \\sqrt{R^2 + (X_L - X_C)^2}$ — Total impedance in an RLC circuit"],"keyPoints":["Power factor is a dimensionless quantity ranging from 0 to 1.","A unity power factor ($PF=1$) occurs in purely resistive circuits where $\\phi = 0$.","Lagging power factor is associated with inductive loads, while leading is associated with capacitive loads.","Higher power factor minimizes current for a given power delivery, reducing $I^2R$ losses."],"advantages":["Reduced transmission line losses","Increased capacity of electrical supply equipment"],"disadvantages":["Requires reactive power compensation (capacitors)","Can lead to voltage instability if poorly managed"],"applications":["Industrial motor drives","Electrical power grid management"],"comparisonTable":[],"additionalInfo":["Option B ($Z/R$) is the secant of the phase angle.","Option C ($V/I$) represents the magnitude of the total impedance $Z$.","Option D ($V/Z$) is equivalent to the current $I$."],"answer":"A is correct — Power factor is defined as the ratio of resistance to impedance (R/Z) in an AC series circuit.","correctedOptions":["$R/Z$","$Z/R$","$V/I$","$V/Z$"],"coreConcepts":["Impedance triangle","Phase angle $\\phi$","Real vs Apparent power"],"crossTopicTip":"Always remember that in an impedance triangle, resistance $R$ is the horizontal component and reactance $X$ is the vertical component; thus, $\\cos(\\phi)$ is always $R/Z$."}