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Your third equation defines impedance. Rearranged to solve for Z, it is: Z = V / I Note that this is exactly Ohms law when V and I are real numbers. In the general case of impedance, all th...
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#2: Post edited
by
Olin Lathrop
·
2022-02-06T23:21:32Z (almost 3 years ago)
Your third equation defines reactance. Rearranged to solve for Z, it is:- Z = V / I
Note that this is exactly Ohms law when V and I are real numbers. In the general case of reactance, all three values can be complex numbers. Put another way, reactance is more generalized resistance, which can be complex too. Resistance is always real.Your top two equations give the <i>magnitude</i> (not the whole complex value) of current for a resistance in series with an inductance (first equation), and a resistance in series with a capacitance (second equation). In both cases, the denominator is the complex reactance.Reactance can be used just like resistance, except that values of voltage and current in the equation can be complex too. This can be a very handy way of performing computations. The complex numbers take into account the phase angles automatically. Alternatively, you can use real numbers, but track the phase angles yourself separately.
- Your third equation defines impedance. Rearranged to solve for Z, it is:
- Z = V / I
- Note that this is exactly Ohms law when V and I are real numbers. In the general case of impedance, all three values can be complex numbers. Put another way, impedance is more generalized resistance, which can be complex too. Resistance is always real. Reactance is usually the imaginary part of impedance, with resistance being the real part.
- Your top two equations give the <i>magnitude</i> (not the whole complex value) of current for a resistance in series with an inductance (first equation), and a resistance in series with a capacitance (second equation). In both cases, the denominator is the complex impedance.
- Impedance can be used just like resistance, except that values of voltage and current in the equation can be complex too. This can be a very handy way of performing computations. The complex numbers take into account the phase angles automatically. Alternatively, you can use real numbers, but track the phase angles yourself separately.
#1: Initial revision
by
Olin Lathrop
·
2022-02-06T15:07:22Z (almost 3 years ago)
Your third equation defines reactance. Rearranged to solve for Z, it is: Z = V / I Note that this is exactly Ohms law when V and I are real numbers. In the general case of reactance, all three values can be complex numbers. Put another way, reactance is more generalized resistance, which can be complex too. Resistance is always real. Your top two equations give the <i>magnitude</i> (not the whole complex value) of current for a resistance in series with an inductance (first equation), and a resistance in series with a capacitance (second equation). In both cases, the denominator is the complex reactance. Reactance can be used just like resistance, except that values of voltage and current in the equation can be complex too. This can be a very handy way of performing computations. The complex numbers take into account the phase angles automatically. Alternatively, you can use real numbers, but track the phase angles yourself separately.