Absolute-value impedance:

There will be times when you will come to know that the impedance of some device or component is a certain number of ohms. For instance, in audio electronics, there exist 8-O speakers and 600-O amplifier inputs. How can the manufacturers give a single number for a quantity which is 2-dimensional, and needs 2 numbers to be completely expressed?

There are 2 answers to this question. First, figures like this refer to devices which have purely resistive impedances. Therefore, the 8-O speaker really has a complex impedance of 8+ j0, and the 600-O input circuit can be designed to operate with the complex impedance at, or near, 600+ j0.

Second, you can at times talk about the length of impedance vector, saying this a certain number of ohms. If you talk about impedance in this manner, you are being ambiguous, as you can have an infinite number of different vectors of the given length in RX plane.

At times, the capital letter Z is used in place of word impedance in the general discussions. This is engineers mean when they say things as Z=50 O or Z =300 O nonreactive.

Z =8 O in this context, if no specific complex impedance can be is given, we can refer to the complex value 8+ j0, or 0+ j8, or 0= j8, or any value on a 1/2 circle of points in RX plane which are at distance 8 units away from 0    j0. This is shown in the given to us. There are an infinite number of different complex impedances having Z=8 O.

Problem:

Name 7 different complex impedances having an absolute value of Z =10.

The pure inductance, pure resistance, and pure capacitance, can be given as 0+j10, 10+j0, and 0- j1 respectively. A right triangle can exist having sides in the ratio of 6:8:10 units. This is true because 6²+8² = 10². Therefore, you may have 6+j8, 6 - j8, 8+j6 and 8 -j6, all complex impedances the absolute value of which is 10 ohms. Certainly, the value Z =10 was chosen for this problem as such a whole number right triangle exists. It becomes a lot messier to do this problem (but not impossible) if Z = 11 instead.

If you are not specifically told what the complex impedance is meant when a single number ohmic figure is quoted, it is best to suppose that the engineers are talking about nonreactive impedances. They are pure resistances, and that imaginary, or reactive, factor is zero. Engineers will speak of nonreactive impedances often, or of complex impedance vectors, as high Z or low Z. For instance, a speaker may be called low-Z and a microphone high-Z.