# Parallel Circuits

In a Parallel Circuit, there are two or more paths for the current to flow. Voltage in parallel circuits is the *same* across each Parallel branch. Each branch current is *inverse* to it’s resistance value, meaning the highest resistance value will have the least current flowing through it.

In parallel circuits, we substitute the current for the sum equals the total rule. The total current in a parallel circuit equals the sum of the branch currents.

**I**t = **I**1 + **I**2 + **I**3… etc.

This is known as Kirchhoff’s current law. The value of current entering a point must equal the value of current leaving that same point.

As stated already, branch current is inverse to branch resistance. another difference in parallel circuits is the way total resistance is calculated. Whereas in a *series circuit* the total resistance is just the *sum* of all resistances, in a *parallel circuit*, the total (or equivalent) circuit resistance is *always less* than the smallest value branch resistance.

Knowing branch current, and total voltage, using Ohm’s law we can find each branch resistance.

**R** branch = **V** / **I** branch

Knowing each branch current, and each branch (total) voltage, we can calculate the equivalent resistance. To keep things simple, we will use the reciprocal method which is as shown below.

**1**/**R**eq = **1**/**R**1 + **1**/**R**2 + **1**/**R**3… etc.

There is also another method for use only with two branches called the *product over the sum*, but seeing as the reciprocal method works for any amount of branches, it would be best to stick to a single method for calculating equivalent resistance (**R**eq).

If you want to calculate an unknown (**R**u) or desired resistance for a certain branch, you can use the following formula.

**R**u = **R**k x **R**eq / **R**k – **R**eq

where **R**u is the unknown you would like to solve, **R**eq is the desired equivalent resistance, and **R**k is the known resistor that will be placed in parallel with **R**u, achieving the desired resistance. This is known as the *product over the difference*.

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