Electrical Engineering is a free introductory textbook to the basics of electrical engineering. See the editorial for more information....  # Parallel Circuits With Resistance, Inductance, and Capacitance

Author: E.E. Kimberly

Each of a number of parallel circuits connected to a common source of voltage acts as if it exists alone. The characteristics of a combination of parallel circuits may best be studied by solution of an example. Fig. 5-19. Parallel Circuits With Resistance, Inductive Reactance, and Capacitive Reactance

Example 5-10. - Four circuits with constants as given in Fig. 5-19 are connected in parallel across a 220-volt, 60-cycle line. Find the total current and its phase-angle displacement from the applied voltage.

Solution. - Since this is a parallel circuit, V is common to all branches and will be taken as the reference. For circuit 1, (i)

For circuit 2, (2)

For circuit 3, (3)

For circuit 4, (4) Fig. 5-20. Vector Diagram for Example 5-10 The vector diagram is shown in Fig, 5-20
The total current is found as follows: The most significant point in Example 5-10 is that, while the arithmetical sum of all the branch currents is 80.6 amp, the actual line current is only 67.2 amp. If there were added another parallel circuit with pure inductance which would take a current 0-j4.38 amp, the sum of all leading and lagging components would be zero and the line current would be 67.03+jO and would be in phase with V. This would be a case of anti-resonance. A practical use for anti-resonance is found in industrial-power distribution. The current used by mills and factories usually lags the line voltage. By adding a condenser in parallel with the load at the factory, anti-resonance may be approached; thus, there will be a reduction in the line current and in the cost of conductors to provide the necessary power.

The instantaneous power is the product of the instantaneous voltage and instantaneous current.

Last Update: 2010-10-06