**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**.

Figure 1 Example of a circuit containing three resistors
connected in parallel |
Figure2 Circuit containing resistors in parallel, equivalent
to Figure 1 |

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

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