Understanding & Calculating Parallel circuit

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UNDERSTANDING & CALCULATING PARALLEL CIRCUITS

EXPLANATION

A Parallel circuit is one with several different paths for the electricity to travel. It's a river that has been divided up into smaller streams. However, all the streams come back to the same point to form the river once again. See figure 1.

The parallel circuit has extremely different characteristics than a series circuit. For one, the total resistance of a Parallel Circuit is NOT equal to the sum of the resistors (like in a series circuit). The total resistance in a parallel circuit is always less than any of the branch resistances. Adding more parallel resistances to the paths causes the total resistance in the circuit to decrease. As you add more and more branches to the circuit the total current will increase. Why? Well remember from Ohm's Law that the lower the resistance, the higher the current.

BASIC RULES

A Parallel circuit has certain characteristics and basic rules summized here:

1. A parallel circuit has two or more paths for current to flow through.
2. Voltage is the same across each component of the parallel circuit.
3. The sum of the currents through each path is equal to the total current that flows from the source.
4. You can find total resistance in a Parallel circuit with the following formula: 1/Rt = 1/R1 + 1/R2 + 1/R3 +... Rt = R (t)otal Note: The formula is not as difficult as it looks. Bear with me.
5. If one of the parallel paths is broken, current will continue to flow in all the other paths.

Let's look at each of these closer to gain an understanding of Parallel circuits.

Keep in mind that the diagrams below represent resistors and a battery. But they can just as easily be any resistance source such as a light bulb or power source such as a wall adaptor.

"1. A parallel circuit has two or more paths for current to flow through."

This is self explanatory. Simply remember that PARALLEL means two paths up to thousands of paths. The flow of electricity is divided between each according to the resistance along each route.

"2. Voltage is the same across each component of the parallel circuit."

You may remember from the last section that the voltage drops across a resistor in series. Not so with a parallel circuit. The voltage will be the same anywhere in the circuit.

"3. The sum of the currents through each path is equal to the total current that flows from the source."

If one path is drawing 1 amp and the other is drawing 1 amp then the total is 2 amps at the source. If there are 4 branches in this same 2 amp circuit, then one path may draw 1/4A (.25A), the next 1/4A (.25), the next 1/2A (.5A) and the last 1A. Don't worry, the next rule will show you how to figure this out. Simply remember for now that the branch currents must tally to equal the source current.

"4. You can find TOTAL RESISTANCE in a Parallel circuit with the following formula: 1/Rt = 1/R1 + 1/R2 + 1/R3 + ...
Before we get into the calculations, keep in mind what we said at the start of this section: "The total resistance of a parallel circuit is NOT equal to the sum of the resistors (like in a series circuit). That said, let's dig into the formula.

We will use a parallel circuit with 3 paths as an example (it can just as easily be 2, 4 or a 1000 resistors in parallel). The power source is providing 10 volts and the value of the resistors are 4 Ohm, 4 Ohm and 2 Ohm.

Let's summize this EXAMPLE for clarity:
Voltage = 10V
R1 = 4 Ohm
R2 = 4 Ohm
R3 = 2 Ohm

Remember that "Rt" means Total resistance of the circuit.
R1, R2, etc. are Resistor one, Resistor two, etc.

Now we will apply the formula above to this example:
1    1    1    1
-- = -- + -- + --
Rt   R1   R2   R3

Therefore:
1    1    1    1
-- = -- + -- + --
Rt   4    4    2

It is easiest to change the fractions into decimal numbers (example 1 divide by 4 equals .25):
1/Rt = .25 + .25 + .5
1/Rt = 1

Now you have to get rid of the 1 on the left side so...
Rt = 1/1
Rt = 1 Ohm

NOW, Let's try a more complex one:

Voltage = 120 Volts
R1 = 100 Ohms
R2 = 200 Ohms
R3 = 1000 Ohms
R4 = 1 Ohms

1/Rt = 1/100 + 1/200 + 1/1000 + 1/1
1/Rt = .01 + .005 + .001 + 1
1/Rt = 1.016
Rt = 1/1.016 = .98 Ohms

(NOTE: There was a miscalculation in previous editions. Thanks to Ron for the corrections)

This is quite a different result than if the circuit were if the resistors were in series (1301 Ohms).

Before we move on to the last rule I want to show you how easy it is to calculate the amperage through each path using OHM'S LAW.

In the example we see a 10 and 20 ohm resistor in parallel with a 10 Volt source. First we figure out the total resistance of the circuit:

1/Rt = 1/10 + 1/20 Rt = 6.67 OhmsNow you know this you can figure out the total amperage (It) using Ohm's Law:

I total (It) = 10V / 6.67 Ohms = 1.5 AmpsTherefore the total amperage between the two resistive paths must equal 1.5 Amps (Rule 3). Now we can figure out exactly what each path is pulling using Ohm's Law once more. Remember that the voltage is the same everywhere in a parallel circuit. So we know the voltage and the resistance:

I1 = 10V / 10 Ohm = 1 A
I2 = 10V / 20 Ohm = .5 A

We figured the total amperage (It) previously, so now we can double check if the figures are correct:

I1 + I2 = It 1A + .5A = 1.5A - checkWe will look at more calculations in future chapters.

"5. If one of the parallel paths is broken, current will continue to flow in all the other paths."

The best way to illustrate this is also with a string of light bulbs in paralallel. If one is burnt out, the others stay lit.

©Copyright 1999 * John Adams

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