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13.4: Resistance and Inductance in Series

Last updated

Mar 5, 2022
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- 13.3: Complex Numbers
- 13.5: Resistance and Capacitance in Series

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The impedance is just the sum of the resistance of the resistor and the impedance of the inductor:

$\label{13.4.1}Z=R+jl\omega .$

$L\omega$ is the reactance. For a pure resistance, the impedance is real, and $V$ and $I$ are in phase. For a pure inductance, the impedance is imaginary (reactive), and there is a 90^o phase difference between $V$ and $I$ .

The voltage and current are related by

$\label{13.4.2}V=IZ = (R+jL\omega )I.$

Further the ratio of the peak (or RMS) voltage to the peak (or RMS) current is equal to the modulus of the impedance, namely $\sqrt{R^2+L^2\omega^2}$ .

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