27.9 - Parallel wiring
Parallel wiring: Circuit wiring that branches.
The same potential difference exists across each
branch.
In parallel wiring, there are junctions where multiple wires come together. A current can
flow into a junction and then divide along different paths. A path between two junctions
is called a branch.
Consider electrons just to the left of junction A in Concept 1. The electrons are moving
to the right when they reach the junction. As they reach it, some turn left into the branch
along the middle wire, while others continue moving straight into the branch around the
outer wire loop. The two flows of electrons, the two currents, rejoin at the junction
labeled B.
Because charge is conserved around a circuit, the sum of the currents flowing into a
junction equals the sum of the currents flowing out. This is an important principle known
as Kirchhoff’s junction rule.
The potential difference is the same across the end points of parallel branches in a circuit. This is a crucial concept required for understanding
the functioning of parallel circuits.
In the circuit on the right, a battery is connected in parallel with the light bulb in the branch AB, and with the light bulbs in the branch CD. The
potential difference is identical across the battery and these two branches. The potential differences do not sum as in a series circuit.
In this circuit, the battery is a 1.5-volt flashlight battery. If you placed a voltmeter’s leads on either side of the battery, you would read a value of
1.5 volts. You would also read the same value if you placed the leads across the middle branch or across the CD branch. The potential
difference across all three branches is identical. This confirms that all three branches are in parallel.
Parallel wiring
Current has more than one path
Potential difference same across
parallel branches·Current may vary from loop to loop
27.10 - Resistors in parallel
To calculate the equivalent resistance of
resistors in parallel: Add the reciprocal of each
resistor’s resistance. The reciprocal of this sum
equals the equivalent resistance.
The equation on the right shows how to calculate the equivalent resistance of resistors
in parallel. First, take the reciprocal of each resistance. Those values are summed. The
reciprocal of that sum is the equivalent resistance of the parallel resistors.
Another equation, also shown to the right, allows you to quickly calculate the equivalent
resistance when just two resistors are wired in parallel. This equation can be derived
from the first with a little algebra.
The example problem on the right shows two resistors, one of 4.0 , the other of 6.0 ,
wired in parallel. To calculate the equivalent circuit resistance of these two resistors,
first invert each value and add these reciprocals. Then, invert that sum. The equivalent
resistance is 2.4 .
We can then calculate the current in the circuit. We must specify the current’s location,
because the current is not the same in all parts of the circuit. In the example problem,
we specify that we are calculating it near the battery.
In this circuit, there is less current in the branches containing the resistors than in the
branch that contains the battery. You use Ohm’s law to calculate the current in the
branches with the resistors. The potential difference across each branch must be the
same as that of the battery, 20 volts. Using Ohm’s law, you determine that there is a
5.0 A current in the branch that contains the 4.0 resistor. (The current equals the
potential difference, 20 V, divided by the resistance, 4.0 .) A similar process enables
you to determine that the current in the middle branch is 3.3 A. Since charge is
conserved, you add these two currents to determine that 8.3 A flows in the branch that contains the battery.