Finding current in a resistor circuit

[mjjaques]

Homework Statement

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.

Homework Equations

Kirchhoff's voltage and current laws.

The Attempt at a Solution

[/B]
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.

 

[berkeman]

I tried Kirchhoff's voltage law and it seems that the current is zero. But I'm not sure if I'm right.

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.

 

[gneill]

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.

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?

 

[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?

 

[gneill]

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?

Right.