why is resistance of a resistor taken in real form and that of capacitor and inductor taken in complex form.why cant the all be real???
MIT 6.002 Circuits and Electronics, Spring 2007
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In a resistor current and voltage are in phase, that is their relation can be expressed with a real number (Resistance, R); in inductors and capacitors current and voltage are out of phase and the only way to express their relation is using a complex number, with a magnitude value and a phase value (Impedance, Z)
I agree. And the reason why v and I are out of phase is that the relation between V and I is differential. Differentiating cosine and sine gives sine and cosine respectively. So their phase is out of 90 degree.
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In the resistor, to apply a voltage in the same, the current through it is changed immediately according to the extent of that tension. In the inductor, when this is initially unloaded, to apply a voltage at its terminals, it behaves like an open switch, so there is no passage of electric current in this first moment, while the tension is at its maximum value. When the inductor loads fully, the current tends to get the maximum value and the voltage at the terminals, to zero. In this way, the current is always in delay with respect to tension. This effect occurs exactly the reverse order on the capacitor, which initially downloaded, behaves like a closed key to apply a voltage, so the current is advanced in relation to the voltage. Because, in the inductor and the capacitor, the voltage being out of phase with the current, we use complex numbers to determine their impedance.
Also, the impedance of a capacitor or an inductor, is a function of the frequency of the voltage or current source(s), whereas the value of a resistance is constant.