Simple circuit - Where is current going?

[Brilliant]

Homework Statement

Find the voltage at V_a.

Homework Equations

Ohm's Law, Current Divider, etc

The Attempt at a Solution

This is the almost identical to the cookie cutter voltage divider, except that there is a resistor on the output. I'm curious if current would even flow through R₂. I guess when you are asked for the voltage at a specific node, it is implied that the common is on ground. So in this case, is the answer going to be the voltage drop between V_a and ground? Which might would be R₂ and R₃ in parallel? or something. I'm very confused.

 

[cepheid]

This is the almost identical to the cookie cutter voltage divider, except that there is a resistor on the output.

No, not really a voltage divider (no two resistors are in series here). And what have you defined as the output?

I'm curious if current would even flow through R₂.

Why wouldn't it?

I guess when you are asked for the voltage at a specific node, it is implied that the common is on ground.

I'm not sure what you mean by "the common", but ground is the reference point relative to which all potentials are measured, yes.

So in this case, is the answer going to be the voltage drop between V_a and ground?

Yes, voltage V_A is defined as the potential difference between the point in the circuit that is labelled V_A and ground.

Which might would be R₂ and R₃ in parallel? or something. I'm very confused.

I can't make sense of this, grammatically or otherwise.

Just use KCL at the node where you've hand-drawn the dot. Assume that some of the current comes into this node from the left (across the branch with R1) and some comes into this node from the right (across the branch with R2). KCL says charge is conserved (can't just disappear) therefore all of the current flowing into this node (the sum of the two currents from either side) is equal to the current flowing out of it (which is across the branch with R3).