Parallel AC Circuits
The methods used in solving parallel AC circuit problems are basically the same as those used for series AC circuits. Out of phase voltages and currents can be added by using the law of right triangles. However, in solving circuit problems, the currents through the branches are added since the voltage drops across the various branches are the same and are equal to the applied voltage. In Figure 131, a parallel AC circuit containing an inductance and a resistance is shown schematically. The current flowing through the inductance, IL, is 0.0584 ampere, and the current flowing through the resistance is 0.11 ampere. What is the total current in the circuit?
Solution:
Since inductive reactance causes voltage to lead the current, the total current, which contains a component of inductive current, lags the applied voltage. If the current and voltages are plotted, the angle between the two, called the phase angle, illustrates the amount the current lags the voltage.
In Figure 132, a 110-volt generator is connected to a load consisting of a 2 μf capacitance and a 10,000- ohm resistance in parallel. What is the value of the impedance and total current flow?
Solution:
First, find the capacitive reactance of the circuit:
Changing 2 μf to farads and entering the values into the formula given:
To find the impedance, the impedance formula used in a series AC circuit must be modified to fit the parallel circuit:
To find the current through the capacitance:
To find the current flowing through the resistance:
To find the current flowing through the resistance:
To find the total current in the circuit:
