An inductor has an impedance of 30.0 Ω and a resistance of 20.0 Ω at a frequency of 80.0 Hz. What is the inductance? (Model the inductor as an ideal inductor in series with a resistor.)?
Impedance for an ideal inductor is: Z j*omega*L For a real inductor with a parasitic resistance modeled in series: Z R + j*omega*L j refers to the imaginary number unit. omega is the angular frequency of the signal. We were given the cycle frequency and we can convert: omgea 2*Pi*f I assume your 30 ohms refers to the magnitude of impedance. Combine both components of the complex number using the Pythagorean theorem. Zmag sqrt(R^2 + (omega*L)^2) And with a substitution: Zmag sqrt(R^2 + (2*Pi*f*L)^2) Square both sides: Zmag^2 R^2 + (2*Pi*f*L)^2 Solve for L: (2*Pi*f*L)^2 Zmag^2 - R^2 2*Pi*f*L sqrt(Zmag^2 - R^2) Resulting expression: L sqrt(Zmag^2 - R^2)/(2*Pi*f) Data: Zmag:30.0 Ohms; R:20.0 Ohms; f:80.0 Hz; Result: L 0.04449 Henries Or, with a convenient prefix: L 44.49 milliHenries
