9 - Branching Currents
In section "7", we saw how two switches in parallel allowed the circuit current to branch and flow through either, or both of them, if they were switched on.
If we connect two lamps in parallel, we also find the circuit current will branch and be divided between them.
In the circuit on the right, the lamps are identical. The yellow and blue currents flowing through them, are therefore the same. These currents combine in the common wires connecting them to the battery.
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Circuit Voltages and Power
It is useful to be able to understand the voltages and power in a circuit too. In section "1" we learnt about Ohms Law and how we can calculate the power being used by a circuit.
Voltage = Amps x Resistance........rule 1
Power = Amps x Volts..................rule 2
We can apply these rules to the circuit above...
We already know the voltage across each of the lamps is the same as the battery voltage. With two similar lamps, we also know the separate yellow and blue currents are the same and these combine to form the total current flowing in the common circuit wires.
Knowing the overall current and battery voltage, we can use rule 2 to calculate the total power that will be required from the battery or power source. With two similar lamps and double the current flowing round the circuit, we can see twice the power will be needed.
If the battery has enough power to deliver this current, each lamp will glow as brightly as if it were connected to the battery on its own. When designing your own circuits, it is important to work out how much power your circuit will need, as it will try to draw this from the power source.
Circuit current will branch when other types of output devices, or circuit components are connected in parallel. The voltage seen across the parallel components will remain the same. However, the separate currents flowing through them, will be determined by their individual resistances.
Resistors in Parallel
In the circuit below, two resistors (R1 and R2) have been connected in parallel and the circuit current split between them.
To find out what is happening to the currents and voltages in the circuit, it can be helpful to represent the two resistors as a single resistor.
The value of the single substituted resistor (R), can be found from this formula:

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Parallel Resistors
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How the Formula was Produced...
As the voltage (V) across R1 and R2 is the same, we can use Ohms Law to say:
V = I1 x R1 and V = I2 x R2
So I1 x R1 = I2 x R2..............1
As the yellow and blue currents combine:
I = I1 + I2..............2
If the two resistors were replaced by a single resistor "R", Ohms law would say:
V = I x R...............3
Using equations 1, 2, 3 and a bit of algebra, we can rearrange to find the value of the single resistor, R, which would take the place of the two parallel resistors R1 and R2.
In the above example, the coloured bands on the resistor tell us: R1 = 1000 Ohms and
R2 = 330 Ohms. Using the formula to replace R1 & R2 with a single resistor, we can calculate R to be 250 Ohms.
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Resistors in Series
In the circuit below, you can see how two resistors (R1 and R2) have been connected in series and the supply voltage split between them.
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When working out what is happening to the voltages and currents in series circuits, it can be helpful to represent the two resistors with a single resistor.
For the circuit currents to be the same, the value of the single substituted resistor (R), can be found from this formula:

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Series Resistors
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How the Formula was Produced...
This time, the current does not branch - it is the supply voltage that is divided between the two resistors:
V = V1 + V2.
The voltages (V1 and V2), as seen across each resistor, will depend on their resistance values. If one is higher than the other, then the voltage appearing across it will be higher. (This will be discussed further in the FastTrack and OnTrack section when "sensor circuits" and "voltage dividers" are being looked at).
The current flowing through each resistor is the same and has been called "I" in the circuit.
Ohms law for resistor 1 says:
V1 = I R1..........1
Ohms law for resistor 2 says:
V2 = I R2..........2
We can also say:
V = V1 + V2.............3
From 1, 2 and 3: V = I (R1 + R2)
For Ohms Law to be true we can therefore see the two series resistors can be replaced by a single resistor (R), with a value = R1 + R2.
In the above example: R1 = 1000 Ohms and R2 = 330 Ohms. Using the formula to replace R1 & R2 with a single resistor, we can calculate R to be 1330 Ohms.