Series Resistance

Series resistors are resistors that are connected end to end in a circuit. A fundamental rule of electronics is that current is constant in any series circuit. This means that the current in all of the resistors in the following figure is exactly the same. If you think about it that makes perfect sense, because any electron that leaves the battery will have to get back to the battery. If there is only one path for it to travel then it’ll be the same through the whole path.

Now how do we figure out what the current is in the above figure? To figure that out we have to understand that the voltage drop through the whole circuit will have to be V or the battery voltage. If this is the case then the sum of the voltage drop through each of the three resistors will have to add up to V. So let’s say that V1 is the voltage drop across R1, V2 is the drop across R2, etc. That give us…

V = V1 + V2 + V3

We don’t know ‘I’ yet but we can use it in the equation to figure out what the Vs are.

V1 = I * R1
V2 = I * R2
V3 = I * R3

So with a little substitution…

V = I * (R1 + R2 + R3)

Well that was a complicated way to figure out that resistors in series can simply be added together to find the total resistance.

So let’s try some real examples. Let’s assume…

V = 10 Volts
R1 = 100 Ω
R2 = 150 Ω
R3 = 250 Ω

The sum of the resistance is 500 Ω. Using Ohm’s law we get a current of 10 V / 500 Ω = 0.020 Amps or 20 mA.

So now if we were to measure the voltage drop across the resistors what would we get…
V = I * R
V1 = 0.020 A * 100 Ω = 2 Volts
V2 = 0.020 A * 150 Ω = 3 Volts
V3 = 0.020 A * 250 Ω = 5 Volts

Adding those together we get the 10 Volts that we started with. So it all works out.

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