Resistance in Series and Parallel

- Sometimes you’ll need to work out the sum of two resistors, their combined/overall effective resistance
- When two resistors are in series, their resistances add
- Two 3 ohm resistors in series are equivalent to a single 6 ohm resistor
- When resistors are in parallel, though, something else happens
- A useful analogy would be some double doors – when one is open, everybody has to squeeze through it, but when you open the second, there’s more space, so people can get through more quickly
- People could get through twice as quickly, so there would only me half as much queuing
- That’s why two identical resistors in parallel have a sum equal to half of one of them…
- What I’m trying to say is that two 3 ohm resistors in parallel are equivalent to a single 1.5 ohm resistor
- The resistors in parallel aren’t always the same value, though: a really narrow door opening next to an already-open wider door would make a bit of a difference, but queue times certainly wouldn’t be halved!

How To Work out Resistances in Parallel

- If the resistors in parallel are identical, halve one of them
- If there are only two resistors, you can do (R1+R2)/(R2*R1)
- If there are more, do 1/Total = 1/R1 + 1/R2
- (The total resistance is the reciprocal of the sum of the reciprocals of the resistances)
- In Physics, we learned that when resistors are in parallel, their conductances add (as opposed to their resistances adding when they’re in series)
- Conductance isn’t covered in AS Electronics, but when you know that conductance is the reciprocal of (one divided by) resistance, the formula is easier to understand/remember
- When you use the 1/Total=… formula, don’t forget that it’s 1/Total. It’s a common mistake to accidentally give the reciprocal of the answer
- I hope I’ve been using the word reciprocal correctly. (Maybe I mean inverse. I’m pretty sure they’re the same, though)

Kirchoff’s Laws

- The (paraphrased) laws are:
- Law 1: The sum of currents going into a junction is the same as the sum of currents going out of the junction
- So, when current encounters a junction where it can split up, the paths with the most resistance will get the smallest current, and most of the current will go the route with the least resistance, but…
- …when the paths meet up again, the currents will combine, and the total will be equal to what the current was before it split up
- Law 2: The total voltage dropped across all the components in the circuit is the same as the supply voltage
- When you’ve got some resistors in series, the ones with the highest resistance will have the biggest voltage drops over them, but…
- …the total of all the volts dropped will be the same as the supply voltage

It boils down to this

- Components in series have the same current through them
- The total current is split between components in parallel
- The total voltage is split between components in series
- Components in parallel have the same voltage across them
- Once you’ve got your head around that, circuits make a lot more sense
- What proportion of the voltage drops across each resistor depends on the ratio of their resistances
- What proportion of the current goes through each path depends on the ratio of the paths’ resistances

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