Impedance Triangle

Definition:

Impedance Triangle is a right angled triangle whose base, perpendicular and hypotenuse represents Resistance, Reactance and Impedance respectively. It is basically a geometrical representation of circuit impedance.

Explanation of Impedance Triangle:

Impedance consists of two components viz. resistance and reactance. Therefore, it can be expressed in these two components. Let the impedance of an alternating current circuit is Z = R+jX where R and X represents the resistance and reactance. It is clear from the expression of Z is that, it is a complex number and hence can be geometrically represented in the same manner as a complex number. The geometrical representation is shown below.

The above triangle OAB so formed is called Impedance Triangle. From this triangle, the magnitude of impedance Z can easily be found using Pythagoras Theorem. The of magnitude of impedance Z is equal to OB and can be find as below.

OB² = OA²+AB²

Z² = R²+X²

Thus, we can say that square of impedance is equal to the sum of square of resistance and reactance.

Z = √(R²+X²)

The angle which Z makes with R i.e. angle between OA & OB may be find as

tanƟ = (X/R)

Hence, Impedance Triangle helps us to find the magnitude as well as the angle of impedance of a circuit.

Significance:

Impedance Triangle is very use if you want to find the value of impedance. This triangle can also be used to find the value of power factor. These values can be found out if the impedance in complex form is known. We will understand this with one example.

Let the impedance of a particular circuit is given as Z = 8+j6. We want to know the magnitude of impedance and power factor. These values may be calculated as below.

Z = √(8²+6²)

    = 10 Ω

To calculate power factor, we will draw impedance triangle (refer the triangle shown earlier in the article. Assign OA = 8 Ω and AB = 6 Ω) and will then find the cosø. Since power factor is equal to cosine of the angle between Z and R, hence this value of cosø is equal to power factor.

cosø = (R/Z)

         =(8/10)

         = 0.8