DC Circuits
RESISTORS IN
PARALLEL
Resistors can be connected such that they branch out from a
single point (known as a node), and join up again somewhere else in the ciruit. This is known as a parallel connection. Each
of the three resistors in Figure 1 is another path for current to travel
between points A and B.


Note that the node does not have to
physically be a single point; as long as the current has several alternate
paths to follow, then that part of the circuit is considered to be parallel.
Figures 1 and 2 are identical circuits, but with different appearances.
At A the potential must be the same for each
resistor. Similarly, at B the potential must also be the same for each
resistor. So, between points A and B, the potential difference is
the same. That is, each of the three resistors in the parallel circuit must
have the same voltage.
[1]
Also, the current splits as it
travels from A to B. So, the sum of the currents through the
three branches is the same as the current at A and at B (where
the currents from the branch reunite).
[2]
By Ohm's Law, equation [2] is
equivalent to:
[3]
By equation [1], we see that all the
voltages are equal. So the V's cancel out, and we are left with
[4]
This result can be generalized to
any number of resistors connected in parallel.
[5]
Since resistance is the reciprocal
of conductance, equation [5] can be expressed in terms of conductances.
[6]
Example
Problem on Resistors in Parallel
Continue to: Combination
Circuits
Self
Test
Return to: DC Circuits Menu
Return to: Physics Tutorial
Menu