# Parallel Connected Resistors

Parallel connected resistors are said to be connected in parallel when both terminals of the resistors are connected to each terminal of other resistance or resistances respectively.

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Unlike previous series resistance circuits, in a parallel resistance network, there is more than one path for current, so it can take more than one way for circuit current.In addition, parallel resistance circuits are classified as current dividers.

Because there is more than one way for the feed current to pass, the current may not be the same on all branches in the parallel network.However, the voltage drop in all resistors in a parallel-resistant network is the same.Next, **Parallel Bound Resistors have** a Common **Voltage.**

Therefore, we can define a parallel resistant circuit defined by the fact that the resistors are connected to the same two points (or nodes) and have multiple current paths connected to a common voltage source.Therefore, the voltage in the resistances of R_{1}, R_{2}, R_{3,} which is connected in parallel, is 12V.

As the following shows, parallel connected resistors are connected to each other in this way:

In the previous series resistance network, we found that the total resistance of the circuit, R _{T,} equal to the sum of all individual resistors added together.Equivalent circuit resistance R _{T} for parallel connected resistors is calculated differently.

Here, the inverse of the algebraic sum that gives the equivalent resistance, as shown, is collected by the mutual (1/R) value of individual resistors instead of the resistors themselves.

Then the opposite of the equivalent resistance of two or more resistances connected in parallel is the algebraic sum of the opposite of individual resistors.

If the two parallel-linked resistances, impedances, or resistance values are of the same value, the total or equivalent resistance, R _{T,} is equal to half the value of a resistance.This is equal to R/2. If the number of parallel resistors with the same values was 3, for three equal resistances in parallel, it would be R/3.

Note that equivalent resistance is always less than the smallest resistance in the parallel network, so total resistance, R _{T} , will always decrease as additional parallel resistors are added.

Parallel resistance gives us a value known as **conductivity,** the G **symbol** and the conductivity unit **Siemens,** which is symbol **S.**Conductivity is the opposite of resistance, (G = 1/R).In order to convert conductivity back into a resistance value, we need to take the total resistance of parallel resistors, the opposite of the conductivity that gives us R _{T.}

Now we know that the resistances connected between the same two points are said to be parallel.But a parallel resistant circuit can take many forms other than the obvious one given above, where we can see several examples of how resistors can be connected in parallel:

The above five different parallel resistant networks may look different from each other, but they are all arranged as **Parallel Connected Resistors,** and therefore the same conditions and equations apply.

### Parallel Connected Resistors Question Sample 1

Find the total resistance of the following resistors connected to a parallel network, R _{T.}

The total resistance between terminals A and B R _{T} is calculated as follows:

This method of reciprocal calculation can be used to calculate any number of independent resistances connected to each other within a single parallel network.

However, if there are only two separate resistances in parallel, then the total or equivalent resistance value can use a much simpler and faster formula to find R_{T. }

To calculate two resistances with equal or unequal values in parallel, this much faster method of total product product is given as follows:

### Parallel Connected Resistors Question Sample 2

Consider the following circuit, which has only two resists in the parallel combination.

Using our formula above for two resistances connected to each other in parallel, we can calculate the total circuit resistance as R _{T:}

An important point to remember about parallel resistances is that total circuit resistance, i.e. R_{T,} will necessarily be smaller than any resistance connected in parallel. If you find the equivalent resistance of parallel connected resistors smaller than any single resistance, you are making mistakes in the calculation.

In our example above, the value of the combination is calculated as follows: R _{T} = 15kΩ , where the value of the smallest resistance is much higher than 22kΩ.In other words, the equivalent resistance of a parallel network will always be less than the smallest individual resistance in the combination.

Similarly, if three or more resistances, each with the same value, are connected in parallel, the equivalent resistance will be equal to R/n; where R is the value of resistance and n is the number of individual resistors in the combination.

For example, six 100Ω resistances are connected in a parallel combination.Therefore, the equivalent resistance will be: R _{T} = R/n = 100/6 = 16.7Ω .But keep in mind that this only works for resistances with the same values.

## Current in Parallel Connected Resistors

The total current that enters a parallel resistant circuit, I_{T,} is the sum of all individual currents flowing in all parallel branches.However, since the resistance value of each branch determines the amount of current flowing in that branch, the amount of current passing through each parallel branch may not necessarily be the same.

For example, although there is the same voltage on the parallel combination, the resistors may be different, so the current passing through each resistance will definitely be different, as determined by the Ohm Act.

Consider the above two resistances in parallel.The current passing through each of the parallel interconnected resistors (I _{R1} and I _{R2)} is not necessarily of the same value as it depends on the resistance value of the resistance.However, we know that the current that enters the circuit from point A must also be disabled at point B.

*Kirchhoff's Current Laws* state that " *the total current from a circuit is equal to the current that is activated – the current is not lost".*Thus, the total current flowing in the circuit is given as follows:

I_{T} = I_{R1} + I_{R2}

Using *the Ohm Act,* we can calculate the current passing through each parallel resistance shown in Example 2 above as follows:

The current flowing in R _{1} resistance is given as follows:

I _{R1} = V _{S} ÷ R _{1} = 12V ÷ 22kΩ = 0.545mA or 545μA

The current flowing in R _{2} resistance is given as follows:

I _{R2} = V _{S} ÷ R _{2} = 12V ÷ 47kΩ = 0.255mA or 255μA

so it gives us the total current I T flowing around_{the }circuit:

I _{ T} = 0.545mA + 0.255mA = 0.8mA or 800μA

and this can also be verified directly using the Ohm Act:

I _{T} = V _{S} ÷ R _{T} = 12 ÷ 15kΩ = 0.8mA or 800μA (same)

The equation given to calculate the total current flowing in a parallel resistance circuit, which is the sum of all individual currents added to each other, is given as follows:

**I _{total} = I _{1} + I _{2} + I _{3} ….. + I _{n}**

Then parallel resistance networks can also be considered **"current dividers",** since the feed current is divided between various parallel branches.Therefore, a parallel resistance circuit with an *N-resistant* network will have N-different current paths while maintaining a common voltage in itself.Parallel resistors can be replaced with each other without changing the total resistance or total circuit current.

### Parallel Connected Resistors Question Sample 3

Calculate individual branch currents and total currents drawn from the power supply for the following interconnected resistors in a parallel combination.

Since the feed voltage is common to all resistors in a parallel circuit, we can use the Ohm Law to calculate the individual branch current as follows.

Next, the total circuit current flowing into the parallel resistance combination will be I _{T:}

This total circuit current value of 5 amps can also be found and verified by finding the equivalent circuit resistance R _{T} of the parallel branch and dividing V _{S} into the supply voltage as follows.

Equivalent circuit resistance:

Then the current flowing in the circuit will be as follows:

## Summarize

It is said that when two or more resistances are connected to each terminal of both terminals, respectively, they are connected in parallel with each other.The voltage on each resistance in a parallel combination is exactly the same, but the currents passing through it are not the same, since this is determined by the resistance values and the Ohm Law.So parallel circuits are current dividers.

Equivalent or total resistance, R_{T} , is found by mutual addition of a parallel combination.

So far we have seen resistance networks connected in a series or parallel combination.In the next content about resistors, we will look at connecting the resistors in both serial and parallel combinations and producing a mixed resistance circuit at the same time.