68CHAPTER 3. REACTANCE AND IMPEDANCE – INDUCTIVERETILELER37°ETIRELIIR37°ZXLXLVoltageImpedanceFigure 3.13: Series: R-L circuit Impedance phasor diagram.Z = R + jXLZ = 40 + j30|Z| = sqrt(402+ 302) = 50ΩZ = arctangent(30/40) = 36.87oZ = 40 + j30 = 50 36.87o• REVIEW:• Impedance is the total measure of opposition to electric current and is the complex (vector)sum of (“real”) resistance and (“imaginary”) reactance. It is symbolized by the letter “Z” andmeasured in ohms, just like resistance (R) and reactance (X).• Impedances (Z) are managed just like resistances (R) in series circuit analysis: series impedancesadd to form the total impedance. Just be sure to perform all calculations in complex (notscalar) form! ZT otal = Z1 + Z2 + . . . Zn• A purely resistive impedance will always have a phase angle of exactly 0o (ZR = R Ω0o).• A purely inductive impedance will always have a phase angle of exactly +90o (ZL = XL Ω90o).• Ohm’s Law for AC circuits: E = IZ ; I = E/Z ; Z = E/I• When resistors and inductors are mixed together in circuits, the total impedance will havea phase angle somewhere between 0o and +90o. The circuit current will have a phase anglesomewhere between 0o and -90o.• Series AC circuits exhibit the same fundamental properties as series DC circuits: current isuniform throughout the circuit, voltage drops add to form the total voltage, and impedancesadd to form the total impedance.3.4Parallel resistor-inductor circuitsLet’s take the same components for our series example circuit and connect them in parallel: (Fig-ure 78,3.14)Because the power source has the same frequency as the series example circuit, and the resistorand inductor both have the same values of resistance and inductance, respectively, they must also