Resistances in series
and 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!
A general rule for several
resistors in parallel
The reciprocal of the total resistance
is the sum of the reciprocals of each individual resistor.
Remember to turn the 1/R bit "upside down" to come
up with the total resistance.