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Home Circuits With Resistance, Inductance, and Capacitance Parallel Circuits With Resist., Inductance, and Capacitance  
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Parallel Circuits With Resistance, Inductance, and CapacitanceAuthor: 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.
Example 510.  Four circuits with constants as given in Fig. 519 are connected in parallel across a 220volt, 60cycle line. Find the total current and its phaseangle 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)
The most significant point in Example 510 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 0j4.38 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 antiresonance. A practical use for antiresonance is found in industrialpower 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, antiresonance 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.


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