I would like to tackle its understanding today to the best of my ability.
The following explanation is adapted from http://physicsnet.co.uk/a-level-physics-as-a2/current-electricity/circuits/
Resistors in series and in parallel
Resistors in Series
When resistors are in series with each other there total resistance is just there individual resistance added together.
Resistors in parallel
When resistors are in parallel with each other there total resistance is found using the equation below.
The purpose of adding them in series is to make the total resistance bigger, while it is smaller in parallel. As more branches are added, you are lowering the resistance, which increases the total current. This is the reason why if you plug so many things to the outlet, the chance of having fire hazard increases!
Current in series and parallel circuits
Conservation of charge – ” the total charge flowing into a junction of wires must equal the total charge flowing out of the junction”.
Kirchoff’s first law – “the sum of the currents flowing into a junction of wires must equal the sum of the currents flowing away from the junction of wires”.
Current in series circuits.
Current works differently than resistors. based on Kirchoff's first law, how much it flows out= how much it flows back in. Since there are no branches, the total current is the same throughout.
This is why I1=I2=I3=I4....
Current in parallel circuits.
The total current flowing from the cell towards the branches in the circuit must always equal the current flowing through each component in the branches of the circuit when they are added together.
Here, we see the current gets branched out into 3 ways. So which mean the total current would be I1+I2+I3 ( remember Kirchoff's first law?)..
This is why Itotal= I1+I2+I3
If the components have different resistances then the current through each component may be different but it when you add them together they must add up to the total amount of current leaving the cell.
Same reason as above: Itotal= I1+I2+I3 and I total must be 0.3A
Potential difference in series and parallel circuits
Kirchoffs second law – ” the sum of the Emf’s in any closed loop in a circuit must be equal to the sum of the potential differences in the closed loop in the circuit”.
Potential difference in a series circuit.
The total potential difference supplied by the cell is divided up between the components. If the components all have the same resistance they will have equal amounts of potential difference across them.
When voltage meets a resistor, its voltage will decrease and its decreased amount will be based on the resistor. In this case, all resistors are the same so they decrease the same amount. However, at the end, they are all end up what was before, which is 12V.
This is why, Vtotal = V1+V2+V3= 12V
*Read this part after you finish the potential difference in a parallel circuit.
-If you think about it, for the following figure, if you add all of the components up, you get 12V, which corresponds to one of the components in the parallel circuit!
For example, if imagine you don't know the voltage for each of the component, but you know the resistor is the same. And you remember that voltage has to be the same (12V), so you could do something like 3x=12, where x=4! You just found the voltage for each of the component.
If the resistance are not equal they may have different amounts of potential difference across them but when added up they must always equal the p.d. supplied by the cell.
Same reason as above. They have to add up to 12V at the end.
Potential difference in parallel circuits.
The potential difference supplied by the cell is the same potential difference as that across each component in the parallel circuit.
Voltage doesn't work like Current. When voltage is branched out, the amount of voltage is the same (it doesn't split up into parts like current. Therefore, its 12V for each component
Thanks http://physicsnet.co.uk/a-level-physics-as-a2/current-electricity/circuits/ for the illustration and explanations. They allow me to understand the magical power that series and parallel circuits embody.
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