Why is the equivalent resistance of a parallel circuit smaller than any of the individual resistance in the connection?

Answer 1

When you add an additional resistor in parallel, there are additional paths which the current can take - making it easier for the current to go from one side to the other.

Answer 2

Reason on it for a moment. Remember Ohm's law?

I = E/R

That says that for current to increase, resistance must decrease (assuming

voltage stays the same).

Now think of a circuit where a voltage source feeds a resistor. There is current

flow. Now add another resistor in parallel with the first. There is another path

for current to flow, so the total current from the voltage source increases. Ohm's

law says for increased current flow, the resistance must have decreased.

So, when you add resistance in parallel, the total resistance always decreases.

So, if we start with a 10 ohm resistor, then add a 100 ohm resistor, without

doing any math, we know the current will be higher than with just the 10 ohm

resistor, so the total resistance will be less than 10 ohms.

Of course, you could start with the 100 ohm resistor, but once they are in

parallel, the electrons don't care what order they were added, the total

resistance is still less than 10 ohms.

Now, if you add a third resistor, say a 5 ohm, the 10 and 100 will conspire to

add current flow and make the total resistance less than 5 ohms.

The rule holds true every time!

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The total resistance is the total 'difficulty' of getting from point-A to point-B ...

the total level of effort, fatigue, and frustration you have to go through in order

to jump across ... which is actually a pretty good representation of the energy

that the electrons lose in traversing the circuit.

Now consider:

Several roads in parallel ... connecting the same two towns ... can always carry

more traffic than the widest single road in the group can.

Analogies are usually pretty poor explanations, but to me, this one is right on.

Answer 3

If you put a voltage across a resistor you get a certain current. If you put the same voltage across two identical resistors you will get twice as much current, simply because you have two resistors.

Here are some some equations.

For a single resistor R₁

V₀= R₁*I₁

For two identical resistors the equation will eventually take the form

V₀= R₀*I₀

Where I₀ and R₀ is the new current and new resistance.

If you have two identical resistors in parallel then you have twice the current.

I₀ = I₁ + I₁

or

I₀ = 2*I₁

or

I₁ =½I₀

If we take

V₀= R₁*I₁

and substitude..

V₀= R₁*½I₀

or

V₀= ½R₁*I₀

Now compare that to the equation

V₀= R₀*I₀

and you can see how...

R₀= ½R₁

so the resistance is half.

Remember resistance is simply a number that relates current to voltage and nothing more.

Answer 4

Without getting into the mathematics of it, the best way to look at parallel resistors is that each resistor provides an additional path for current to flow. Because of this, the equivalent resistance CANNOT be higher than the lowest value resistor in the parallel combination. And since each additional resistor provides an alternate path for more current to flow than would flow through the smallest value resistor, the equivalent resistance will ALWAYS be lower than the value of the lowest resistor.

Answer 5

That's true only in a parallel circuit, and it's fairly easy to understand

with the help of a simple analogy:

Several roads in parallel ... connecting the same two towns ... can always

carry more traffic than the widest single road in the group can.

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Similarly, the total resistance of a series circuit is always higher than the

highest resistor in the circuit.

Several roads in series ... all the pieces of road you have to drive through to

get from one town to another ... are always harder to get through altogether

than the narrowest, bumpiest single piece of road in the string is.