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what is impedance??


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  • 2 weeks later...

For a resistor the relationship between voltage across it and the current through it is very simple - the current is always proportional to the voltage (V = IR). We say that an alternating current through a resistance will develop an alternating voltage across it which is in phase with the current, or that there is zero phase difference.

For a capacitor or inductor though, the relationship is more 'complex' (see what I did there?). For example, the current through a capacitor is proportional to the rate of change of the voltage across it. This means that a sinusoidal alternating current through the capacitor will be 90 degrees out of phase with the resulting sinusoidal voltage developed across it.

This phase shift means that a simple value of resistance is not enough to completely describe the behaviour of a capacitor. Instead we use a complex number, which is really a vector encapsulating both 'phase angle' and 'magnitude' information.

This complex number is called impedance. It is analagous to resistance, in that it describes the relationship between current through and voltage across some device, but it includes phase information as well as magnitude. You can think of resistance R as being a complex number (R + 0j) with an angle of zero and magnitude of R. In other words, a resistance is an impedance with no imaginary part. Thus a resistance is an impedance through which current remains in phase with and in direct proportion to voltage across it.

Ohm's law can be applied using impedances instead of resistance. If impedance is represented by Z, then V = IZ.

Just like resistances, impedances connected in series have a combined impedance of Z = Z1 + Z2 + ... + Zn

Parallel impedances are treated as you would treat parallel resistances:
1 / Z = 1 / Z1 + 1 / Z2 + ... + 1 / Zn

One more complication: the impedance of a reactive component (like a capacitor) varies with frequency. For a given frequency f (Hz), the impedance of a capacitance C (Farads) is Zc = -j / (2 Pi f C). Note that this a purely imaginary value! That's describing the fact that the current in a capacitor is always 90 degrees out of phase with the voltage across it.

Better brush up on your complex arithmetic. It will be worth it in the end.

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