Finding current in a resistor circuit

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Homework Help Overview

The discussion revolves around a resistor circuit where participants are examining the effects of placing a jumper between two nodes, A and B. The problem involves calculating the voltages at these nodes and the current through the jumper, given specific resistor values.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the implications of connecting a wire between nodes A and B, noting that this would equalize the voltages at these points. There is curiosity about finding the current without relying solely on Kirchhoff's laws. Some participants explore the symmetry of the circuit and the voltage divider concept to understand the behavior before and after the jumper is connected.

Discussion Status

The conversation is ongoing, with participants sharing insights about the equal voltages at nodes A and B prior to connecting the jumper. There is acknowledgment of the potential differences in current if the jumper were replaced with a resistor. No consensus has been reached, but several productive lines of reasoning have been introduced.

Contextual Notes

Participants are working within the constraints of the problem, focusing on the specific resistor values provided and the implications of connecting the jumper. There is an underlying assumption that the circuit behaves according to standard electrical principles, but the nuances of current flow and voltage relationships are being actively explored.

mjjaques
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Homework Statement


hwproblem.jpg


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.
 
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mjjaques said:
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. :smile:
 
Last edited:
mjjaques said:
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?
 
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?
 
mjjaques said:
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.
 

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