Mesh Current Analysis: Find Current Through Short Circuit Wire

[Tekneek]

Homework Statement

I need to find the Current through short circuit wire (between a and b).

Homework Equations

All the resistor values are same, 100 Ohms
V1 = 5V
V2 = 10V

The Attempt at a Solution

Loop A
ia*(R2+R4+R1) - ib*(R4) = 5

Loop B
10 + (ib-ia)*R4 + ib*R3 = 0
ib*(R4+R3) - ib*R4 = -10

After plugging in all the values,

300ia - 100ib = 5
-100ia + 200ib = -10

ia= 0, ib= 0.05 Amps

Current through the circuit is same as ib because the current is not going to flow through R5.
But the problem is I don't think it is possible for ia to be 0...

 

[NascentOxygen]

ia= 0, ib= 0.05 Amps

That looks right.

If V2 were much higher, say 60v, it would be forcing current into source V1, similar to charging a battery. So there is some point where V1 ceases to supply current, but before its current goes negative. This point occurs when V2=10v here.

Yes, the current in the s/c is that current in R3.

 

[Tekneek]

That looks right.

If V2 were much higher, say 60v, it would be forcing current into source V1, similar to charging a battery. So there is some point where V1 ceases to supply current, but before its current goes negative. This point occurs when V2=10v here.

Yes, the current in the s/c is that current in R3.

Thanks. But how does V1 stop supplying current?

 

[NascentOxygen]

Thanks. But how does V1 stop supplying current?

When it finds itself connected to a voltage that's exactly equal to its own voltage. Current can flow neither IN nor OUT.

 

[rezeew]

Hello, based on your calculations, it appears that the current through the short circuit wire (between points a and b) is 0.05 Amps. This means that the current is flowing through the circuit in a clockwise direction, as determined by the direction of the current in loop B. However, it is important to note that this solution assumes ideal conditions and may not be accurate in a real-world scenario. In addition, it is possible for the current through the short circuit wire to be 0 if the resistance of the wire itself is very low. It is always important to double check your calculations and assumptions in order to ensure accuracy in your analysis.