# Finding current in a resistor circuit

1. Oct 12, 2015

### mjjaques

1. The problem statement, all variables and given/known data

There are several parts, but the part I'm stuck on is: what happens if a jumper is placed from node A to node B? Calculate V_A and V_B, and magnitude and direction of the current through the jumper. The resistor values are R1=R2=2 kohms, R3=R4=1 kohm.

2. Relevant equations

Kirchhoff's voltage and current laws.

3. The attempt at a solution

Okay, so I know that connecting a wire between A and B will make V_A=V_B. I was wondering if there's an intuitive way to find the current quickly without using Kirchhoff's loop rules. I tried Kirchhoff's voltage law and it seems that the current is zero. But I'm not sure if I'm right.

2. Oct 12, 2015

### Staff: Mentor

Correct. Once you short the middle part, you can combine the upper resistors into their parallel combination value, and the same with the lower ones.

If you used a resistor instead of a shorting wire to connect A to B, the answer might be different.

Last edited: Oct 12, 2015
3. Oct 12, 2015

### Staff: Mentor

You could take advantage of the symmetry of the situation. Pencil in the given resistor values on the diagram. Can you "see" what the values of V_A and V_B will be (before connecting the jumper betwixt them)? Does that suggest anything about what the jumper current might be once it's connected?

4. Oct 12, 2015

### mjjaques

So before connecting the jumpers, V_A and V_B are already equal, using the voltage divider equation right? They're both 2.5 V. If they weren't equal before, would there be a current through the jumper?

5. Oct 12, 2015

Right.