Parallel Circuits

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Part 1: Fundamental Concepts: Parallel Circuits

The previous section discussed series circuits.  There is another common way to connect electrical components.  It is called a parallel connection.  When electrical components are connected in parallel, they are arranged so that all of the components are connected across the same two points in a circuit as shown in the following figure.  In this case, the tops of R1, R2 and R3 are connected to one point (the positive terminal of the voltage source) and the bottom of the resistors are all connected to another point (the negative terminal of the voltage source).

Schematic of three resistors in parallel.

Figure 1. Three resistors in parallel.

When dealing with a series circuit, we concerned ourselves with the voltage drops that appeared across the individual resistors due to the common current that was flowing through them.  In the parallel circuit shown in Figure 1, the voltage across each resistor is the same.  The current flow through each leg, or branch, of the circuit is what we are interested in.

To help sort this out, the figure below is the same as Figure 2, with additional annotation added to label the paths where the current will flow.

Schematic of three resistors in parallel with the branch currents labeled.

Figure 1. Three resistors in parallel with current flow labeled.

In Figure 2, the total amount of current flowing, Itotal, is shown both leaving and returning to the voltage source.  The three branch currents, one for each resistor, are shown as I1, I2, and I3.  Given that current cannot be created or destroyed,  Itotal = I1 + I2 + I3.  In other words, the current that leaves the voltage source is divided among the three legs of the circuit and then recombines as it returns to it.  The question then is, how does it divide?  Each branch’s current can be found by applying Ohm's law to that branch.  The total current can then be found by summing each branch current.

                        I = V / R                                ;Ohm's law

                        I1 = 6/100 = 0.06A                ;Put in V and R1

                        I2 = 6/200 = 0.03A                ;Put in V and R2

                        I1 = 6/300 = 0.02A                ;Put in V and R3

                        Itotal = 0.06 + 0.03 + 0.02    ;Sum branch currents

                        Itotal = 0.11A                        ;The total current

Knowing the total current flow into the the parallel group of resistors, as well as the voltage across the parallel group, we could find the equivalent resistance of the three parallel resistors by using Ohm’s Law.  This is discussed in the next section.

Key Concepts

• In a parallel circuit, the current into the parallel connected group divides between the branches.

• The amount of current in each branch can be found using Ohm’s Law.

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copyright © 2021 John Miskimins