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Theoretical foundations of electrical engineering

Solving problems in electrical engineering- Equivalent transformation of resistances star (wye)/delta (triangle)

Suppose you want to calculate the circuit shown in the figure below:

Equivalent transformation of resistances star (wye)/delta (triangle)

Calculation can be performed with one of methods for calculating an electrical circuit. But as in the scheme, there is only one power supply; the most rational way is to use Ohm's law. It should be noted that an attempt to determine the total circuit resistance is ineffective, as there is no consistent or parallel-connected resistors. You can solve the problem by using the transformation of the delta resistances to the equivalent star.

The delta and star resistances are shown below:

Equivalent transformation of resistances star (wye)/delta (triangle)

If at replacement of one of these schemes with potentials of similar points and flowing to them currents do not change, there will be no changes in the external circuit. In this case, we say that the schemes are equivalent.

It can be shown that the condition of equivalence is the following equations.

When transforming a delta to a star:

Equivalent transformation of resistances star (wye)/delta (triangle)

When transforming a star to a delta:

Equivalent transformation of resistances star (wye)/delta (triangle)

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