Deriving the Equivalent Resistance Formulas for Parallel and Series Circuits

In this video the equivalent resistance formulas are derived from the fundamental concepts of the conservation of energy, the conservation of charge and the definition of resistance (R=V/I).

[@TheRandomQubeofficial]

Great work!

[@eatalay6240]

I'd like to point out that the direction of the current in the video is the opposite of what it should be. Great video though!

[@marcolee1382]

Amazing video

[@zhh174]

Awesome video. But can you explain a bit on why v=v1+v2?

[@TheBrainFiller]

It’s basically just conservation of energy, the energy of the cell/battery needs to go somewhere and the only two places it can go is resistor 1 or resistor 2. Why is it just conservation of energy? Recall that volts are joules/coulomb, so we’re essentially just dealing with energy. If some other aspect is confusing you, let me know. Just anticipating a question here: you might then wonder, in the parallel circuit case why is the voltage over both components the same as the voltage over the cell? Doesn’t that break energy conservation? No, it doesn’t. This is where the other part of the definition of volts comes in. Volts are joules per coulomb, that is a cell gives each bit of charge some energy. But as the charge travels throughout the circuit some of it goes down through resistor 1 and the rest goes through resistor 2. So energy needs to conserved and it is for each individual charge. Each charge gives the energy it was given to the resistor it happens to pass through.

[@zhh174]

@@TheBrainFiller thanks for your elaborative answer. Appreciate for efforts

[@dakshbhati681]

Ye so much eff9rt😢

[@malcolm824]

Consider Kirchoff's Laws

[@allgameschamp4569]

thanks alot

[@user-ub1qi3ye5k]

Great

[@hamzamohamed2929]

I can't understand why R equavelnt is in fraction(parallel )and I see that's not the rule of R quavilent that's the rule of Intensity when v is constant in parallel

[@arprogames]

In parallel combination, the potential difference is same across all resistors so we just need to find relation between current and resistance. I.e, According to ohm's law, V = RI So, I = V/R Here, you can see that resistance reciprocates. Since V is same so it'll just cancel out and you'll get the result 1/R P.S: I haven't derived as he did in the video

[@TheBrainFiller]

Thanks for replying, somehow I missed this one. Yeah, we basically agree, the point is voltage is constant over the resistors in parallel and the current must add by conservation of charge and since current is related to voltage and resistance by I=V/R, we can that the resistances add in their reciprocal (cause V cancels out)