Resistance in series Summary for resistance in series Resistance in Parallel How can more resistance equal less resistance? A worked example A general rule for several resistors in parallel

When an electric current flows in a circuit, the wires and components in the circuit naturally offer a resistance to the movement of electrons in the circuit. This is true in any situation where electricity moves through a material. Resistance can be thought of as the atoms in the circuit getting in the way of the electrons as they move through the circuit. The more the path of the electrons is blocked, the greater will be the resistance in the circuit.

Generally, wires are made of metals with low resistance, so as not to impede the passage of the electrons, but resistors are made of materials that impede the passage of electrons to some extent, releasing the energy carried by the electrons usually as heat or light. Any appliance that runs on electricity is a resistor by definition.

Resistors can be placed in circuits in two ways, in series, that is one after the other and in parallel, next to each other. Resistance varies dramatically if the resistors are in series or in parallel. The total resistance of a circuit with resistors in series is equal to the sum of the resistors. Whereas the total resistance of a circuit with resistors in parallel, is actually less than that of each of the individual resistors!

Resistance in series
In a hurdles race one obstacle slows you down and each extra obstacle slows you down even more. This is also the case with resistors - to find the total resistance in a circuit where the resistors are in series, you just add up the resistor values.

As an example, if there are four resistors, 10Ω, 50Ω, 25Ω and 12Ω, in series the total resistance is 10Ω + 50Ω + 25Ω + 12Ω = 97Ω.

Summary for resistance in series
For resistors in series, the total resistance is the sum of the individual resistances.

Resistance in parallel
When resistances are in series, the total resistance is the sum of all the resistances, but when they are in parallel the situation is quite different. In this illustration there are three equal value resistors in parallel.

This is something like being in a supermarket; if only one checkout is open the flow of customers is slowed, but as others open up the flow can be spread, increasing the number of customers that can pass through. When resistors are connected in parallel, the total resistance decreases to less than the smallest resistance!

How can more resistance equal less resistance?
This is difficult to imagine, but here is the mathematical explanation.

From the above diagram, you can see that the current divides between the resistors then joins again after passing through the resistors. The voltage remains the same across the whole system.

Now you can use Ohm's Law . If the three resistors are R₁, R₂ and R₃, the current through each is I₁, I₂ and I₃. The voltage is the same so V₁ = V₂ = V₃. From Ohm's Law, current is equal to voltage divided by resistance or I = V/R.

What you know so far is I₁ = V/R₁ and I₂ = V/R₂ and I₃ = V/R₃. This is where you use your mathematical skills.

The total current is I, and the overall voltage is V so:
I = V (1/R₁ + 1/R₂ + 1/R₃); then I/V (which is 1/R) = 1/R₁ + 1/R₂ + 1/R₃

This is the formula for resistors in parallel:

A worked example
Find the total resistance of two resistors, one of 30Ω and another 15Ω in parallel, using the formula for two resistors (1/R = 1/R₁ +1/R₂)

1/R = 1/30 +1/15
1/R = 1/30 + 2/30 = 3/30 = 1/10.
1/R = 1/10

By then finding the reciprocal (turning both upside down) - R = 10Ω. Note that this is smaller than either of the two resistors!

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