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.