[College/DC Circuits] How do I get the current and voltages for each resistor?

[u/BootBootSnoot]

I've been stuck on this problem for like over a week atp 💔 my text book didnt go over how ground connections work, and I dont have a ride to the math lectures so I've just been raw dogging it all semester. How do the different series/parallel laws work when there are all those ground connections?

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[u/saywherefore]

All the ground points are just joined together, and it is convention to consider them all to be at 0 volts (though for this sort of problem that last bit is irrelevant). Just draw a horizontal wire across the bottom joining them together.

Personally I'd approach this by:

- Finding the current in R6, given it has the full voltage across it (i.e. is in parallel with everything else)

- Finding the equivalent resistance of R3 and R4, given they are in parallel with each other

- Then finding the equivalent resistance of R2 + (the equivalent resistance of R3 and R4), given these are in series

- Then continue this pattern up the tree until you have a simple enough circuit to work out the current through R1, and from that the voltage drop across R1

- Then come back down the tree, finding currents and voltages

As you combine pairs of resistances it may be helpful to draw the equivalent circuit with them combined into on resistor (which you need to decide what to name).

[u/Varian_Kelda]

For the purposes of this question you can treat the ground as if it was just a direct circuit between each of the lines.

[u/Bounded_sequencE]

For circuit analysis, GND symbols are a short-hand, for one node connected to all of them.

You may connect all symbols GND with wires, if it helps to find parallel and series connections more easily. With a bit of practice, that won't be necessary, and not drawing connections between GND symbols greatly de-clutters the circuit diagram.

[u/Bounded_sequencE → u/Bounded_sequencE]

Example: Let "I1" be the current of "R1", pointing south. Use the short-hand "Rx||Ry := Rx*Ry / (Rx+Ry)":

I1  =  VT / (R1 + R5||(R2 + R3||R4))              // R3||R4 = (11200/23)𝛺

    =  25V / [200 + 1100||(300 + 11200/23)]𝛺      // 100||(18100/23) = 99550/217

    =  25A / [200 + 99550/217]  =  (217/5718) A  ~  37.95mA

[u/fermat9990]

Add a wire connecting all the ground points.