Impedance and the Phasor Diagram

AC impedance is the gauge of opposition a circuit presents to current each time a voltage is applied. In a more quantitative sense, it is the ratio of voltage to current within alternating current. Impedance can be extended to the idea of AC circuit resistance and include both phase and magnitude.
Impedance, measured in Ohms, is the effective resistance to current flow around an AC circuit containing resistances and reactance.
So for a purely resistive circuit the alternating current flowing through the resistor varies in proportion to the applied voltage across it following the same sinusoidal pattern. As the supply frequency is common to both the voltage and current, their phasors will also be common resulting in the current being "in-phase" with the voltage, ( $\theta = 0$ ).
In other words, there is no phase difference between the current and the voltage when using an AC resistance as the current will achieve its maximum, minimum and zero values whenever the voltage reaches its maximum, minimum and zero values as shown below.
Sinusoidal Waveforms for AC Resistance
Fig. 1: Sinusoidal Waveforms for AC Resistance
This shows that a pure resistance within an AC circuit produces a relationship between its voltage and current phasors in exactly the same way as it would relate the same resistors voltage and current relationship within a DC circuit. However, in a DC circuit this relationship is commonly called Resistance, as defined by Ohm's Law but in a sinusoidal AC circuit this voltage-current relationship is now called Impedance. In other words, in an AC circuit electrical resistance is called "Impedance".
In both cases this voltage-current ( V-I ) relationship is always linear in a pure resistance. So when using resistors in AC circuits the term Impedance, symbol $Z$ is the generally used to mean its resistance. Therefore, we can correctly say that for a resistor, DC resistance = AC impedance , or $R = Z$.

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