#### Parallel Circuits - Combinations

Ohm's Law is used to solve circuit problems which may contain all three elements: resistors, inductors, and capacitors. These circuits are sometimes called R LC circuits with R for resistance, L for inductance and C for capacitance. The general form of Ohm's Law applied to R LC circuits states:

Voltage = Current x Total Impedance or E = I times R where;

I = current in amps
R = total impedance in ohms

Total impedance is the result of combining impedances of the resistive, capacitive and inductive components of the circuit. However, remember, the resistance, inductance and capacitance are not in phase so they must be added vectorially. They cannot be added directly. When a circuit contains resistors, capacitors, and inductors in parallel, total current flow is obtained by vector addition of current flow for each element. Currents in this case add vectorially in the same orientation as the voltage in the series circuit.

In this case, the angle between the current due to pure resistance, IR, and the total or source current, IS, is the phase shift angle, for the circuit.

For parallel R LC circuits, impedances do not add vectorially as in the series case. Total impedance must be obtained by dividing source voltage by total current.

EXAMPLE 3.11 Parallel Combination R LC Circuit

For the circuit shown, determine the current flow in each element, the source current, the true power, and the apparent power.

Use Ohm's Law for each element of the parallel combination. (Note the voltage across each element is the same for parallel connected loads.)

Determine the source current and phase angle by vector addition.

To find the power factor, divide the amps flowing through the resistance by the total current in amps from the source: