Parallel Circuits With Resistance and Inductance

Author: E.E. Kimberly

When circuit parts with resistance and inductance are connected in parallel to a common source of alternating voltage, the current in each parallel part will have the same magnitude and phase relation to the applied voltage as if each circuit existed alone. The total current drawn from the source will be the vector sum of the currents in the parts that are in parallel. Inasmuch as the applied voltage is common to all the circuit branches, it is customary to lay out the voltage vector horizontally and to refer all current vectors to it.

Example 5-5. - In Fig. 5-11 are represented three branches of a circuit with resistances and 60-cycle reactances which are connected in parallel to a 220-volt, 60-cycle line. The resistances and reactances have the following magnitudes:

Find the current in each branch. Find the total current taken from the line and its phase displacement from the applied voltage.

Solution. - In branch 1,

(1)

Fig. 5-11. Circuit With Resistances and Inductances in Parallel In branch 2,

(2)

In branch 3t

(3)

The current I taken from the line may be found by combining the components of the currents in the branches, as follows:

The vector diagram is shown in Fig. 5-12.

Fig. 5-12. Vector Diagram for Example 5-5