Hi. I'm relatively new to electrical engineering and circuit analysis. So, I'm having a bit of trouble with series-parallel circuits and determining when the rules do and do not apply. I've looked through my notes and textbook and searched around and I think I'm on the right track, but could use some feedback.

I've attached an image of the circuit that I'm working with (the colored wires are just to help me easily identify what is in series and what is in parallel). I know that the current through RL1 is 20mA, RL2 is 10mA, and the total current (IT) is 50mA. I also know that the voltage across RL1 is 60V and RL2 is 20V. I need to find the values of R1, R2, and R3. Here's what I have so far:

RT (total resistance) = ((R1+(R2//RL2))//RL1)+R3
RT = 1.44k ohms

RL1 = 60V/20mA = 3k ohms
RL2 = 20V/10mA = 2k ohms

Since components in parallel have the same voltage, and I know that RL1 is 60V and RL2 is 20V, would that mean that R2 is also 20V? And would that make R1 20V, as well, since (R1+(R2//RL2)) is in parallel with RL1, thus making the total voltage across those three components 60V?

Because the sum of currents through a parallel circuit add up to the total current, which is 50mA, and 20mA is flowing through RL1 and 10mA is flowing through RL2, would that mean that the current through R1 and R2 would be 10mA, each? And does that mean that the total current enters R3?

Assuming that all of the above is correct (or, even if it's not), how would I find the voltage across R3? Would that be 10V? Or maybe the total voltage?

Thanks in advance for the help.

 

Since components in parallel have the same voltage, and I know that RL1 is 60V and RL2 is 20V, would that mean that R2 is also 20V?

Yes, because RL2 is in parallel with R2

And would that make R1 20V, as well, since (R1+(R2//RL2)) is in parallel with RL1, thus making the total voltage across those three components 60V?

Think about that. If the total voltage across R1 + (R2||RL2) is 60 V, and the voltage across R2||RL2 is 20 V, how do you figure that the voltage across R1 can be 20 V?

Because the sum of currents through a parallel circuit add up to the total current, which is 50mA, and 20mA is flowing through RL1 and 10mA is flowing through RL2, would that mean that the current through R1 and R2 would be 10mA, each? And does that mean that the total current enters R3?

This makes no sense.

The current at a junction has to sum to zero (meaning that the current into it must equal the current out of it).

So if you have 50 mA coming from the source into the junction with R1 and RL1, and 20 mA goes on to RL1, what do you know about the current in R1?

Apply that same reasoning to the current coming out the bottom of R1 and the currents that flow into the top of RL2 and R2.

Assuming that all of the above is correct (or, even if it's not), how would I find the voltage across R3? Would that be 10V? Or maybe the total voltage?

The voltage drops around any closed loop must sum to zero. Or, the voltage drop between any two points must be the same regardless of the path taken (assuming we are dealing with conservative electric fields, which we are in this case).

So what is the voltage of the top node relative to the bottom node along the path through the battery?

What is the voltage of the top node relative to the bottom node along the path through R3 and RL1?

 

Think about that. If the total voltage across R1 + (R2||RL2) is 60 V, and the voltage across R2||RL2 is 20 V, how do you figure that the voltage across R1 can be 20 V?

I think I see what you're saying. So, in the same sense that (R1+(R2//RL2))//RL1 can be seen as a single resistor in series with R3, R2//RL2 can be seen as a single resistor in series with R1. Because of this, R2 and RL2 are not 20V, each, but rather 20V as a single component. So, that would make R1 40V, right?

The current at a junction has to sum to zero (meaning that the current into it must equal the current out of it).

So if you have 50 mA coming from the source into the junction with R1 and RL1, and 20 mA goes on to RL1, what do you know about the current in R1?

So, with 20mA going into RL1, 30mA must go into R1, right? Since we're putting 50mA into the junction at R1 and RL1. Then the current will split again into R2 and RL2.

 

I think I see what you're saying. So, in the same sense that (R1+(R2//RL2))//RL1 can be seen as a single resistor in series with R3, R2//RL2 can be seen as a single resistor in series with R1. Because of this, R2 and RL2 are not 20V, each, but rather 20V as a single component. So, that would make R1 40V, right?


So, with 20mA going into RL1, 30mA must go into R1, right? Since we're putting 50mA into the junction at R1 and RL1. Then the current will split again into R2 and RL2.

I think you've got the idea. Keep going.