Electrical Engineering ⇒ Topic : Series-to-Parallel Conversion and Vice-Versa

Series-to-Parallel Conversion and Vice-Versa

In many circuit applications, it is desired to convert series-connected parameters to the equivalentparallel-connected parameters and vice-versa. Fig. (a) shows equivalent RL series and RL parallel circuits. The series circuit has resistance R_s and reactance X_s while the parallel circuit has resistance R_p and reactance X_P. Since the two circuits are equivalent, they must have equal impedance (Z) or admittance (Y) and phase angle Φ. This general principle can be applied while carrying out the conversion

                                              FIGURE (A)

The same principle can be applied to two RC circuits. But an RL circuit cannot be made equivalent to an RC circuit. It is because even if the phase angles were made numerically equal, one of them would be an angle of lag and the other an angle of lead.

Note. We can easily develop formulas for series-to-parallel conversion and vice-versa. However, there is no need of remembering such formulas in view of the general principle explained above. The general principle discussed above gives more insight than the derived formulas for above conversions