L10 & 11 - Series and Parallel Circuits 2

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If two (or more) resistors are connected in series, they give a higher resistance than any of the resistors by itself.
The effect is the same as joining several lengths of resistance wire to form a longer length.
If resistors R₁ and R₂ are in series, their combined resistance R is given by this equation:

There is an example on the right. For three or more resistors, the above equation can be extended by adding R3 ... and so on.

If two (or more) resistors are connected in parallel, they give a lower resistance than any of the resistors by itself.
The effect is the same as using a thick piece of resistance wire instead of a thin one.
There is a wider conducting path than before.
If two resistors R₁, and R₂, are in parallel, their combined resistance R is given by this equation:

To solve problems about circuits, you need to know the basic circuit rules on the previous spread.
You also need to know the link between p.d. (voltage), current, and resistance.
This is given below.

In the circuit on the left, the battery gives electrons potential energy. In the lamp, this is changed into thermal energy (heat) and then radiated.
Power is the rate at which energy is transformed (changed from one form to another). The SI unit of power is the watt (W):

The battery on the right is supplying 5 joules of energy every second, so its power is 5 watts.
The lamp is taking energy at the same rate, so its power is also 5 watts.
Appliances such as toasters, irons, and TVs have a power rating marked on them, either in watts or in kilowatts:

1 kilowatt (kW) = 1000 watts

Some typical power ratings are shown below. Each figure tells you the power the appliance will take if connected to a supply of the correct voltage. For any other voltage, the actual power would be different.

For circuits, there is a more useful version of the power equation. If a battery, lamp, or other component has a p.d. (voltage) across it and a current in it, the power is given by this equation:

For the battery: power = p.d. X current
= 12V X 2A = 24W
For lamp A: power = p.d. X current
= 8V X 2A = 16W
For lamp B: power = p.d. X current = 4V X 2A = 8W
The lamps are the only items getting power from the battery, so their total power (16W + 8W) is the same as that supplied by the battery (24W)

The equation power = p.d. X current is a result of how the volt, ampere, coulomb, joule, and watt are related. The following example should explain why.
Here are two ways of describing what is happening on the right:

General description Scientific description

Each coulomb of charge gains p.d. = 12 Volts

12 joules of energy from the battery

2 coulombs of charge leave the current = 2 amperes

Battery every second

So 12 X 2 joules of energy leave power = 24 watts

the battery every second.

If the power of an appliance is known, the energy transformed in any given time can be calculated by rearranging the first equation on the opposite page like this:

For example, if a 1000 W heating element is switched on for 5 seconds (s): energy transformed = 1000 W X 5 s = 5000 J. So the heating element gives off 5000 J of thermal energy.
As power = p.d. X current, the above equation can also be written like this:

Energy transformed = p.d. X current X time
= 12V X 2A x 60s = 1440 J
In this case, all the energy is transformed into thermal energy, so the heater produces 1440 J of thermal energy.

8.10---What-is-a-Kilowatt-hour.mp4

8.10---What-is-a-Kilowatt-hour.mp4

8.10---Series-and-Parallel-Circuits.docx

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