Question about independent loop in a circuit

[Dethrocutionx]

I just had a question pertaining a circuit that consists of 3 loops in the attached picture:

The textbook states that the loop inside with the 50[V] source is independent of the rest of the circuit, but I have a hard time rationalizing it. The only reason I feel it is the case is because the current induced from the source travels in the loop and at the end of the loop, has to choose between the outside loop with a resistance and a short circuit that connects to the 50[V] source once again, so it chooses the latter. Is my reasoning correct?

Thanks

 

[gneill]

I just had a question pertaining a circuit that consists of 3 loops in the attached picture:

The textbook states that the loop inside with the 50[V] source is independent of the rest of the circuit, but I have a hard time rationalizing it. The only reason I feel it is the case is because the current induced from the source travels in the loop and at the end of the loop, has to choose between the outside loop with a resistance and a short circuit that connects to the 50[V] source once again, so it chooses the latter. Is my reasoning correct?

Thanks

Your reasoning is pretty good. Note that the "choice" the current makes concerns a wire segment (your short circuit) that has the same potential at both points where the loop uses it. There is no potential difference to drive the current out into the external circuit.

For additional rationalization "ammunition", consider that you can move the connection points of things along a wire any way you wish without changing the circuit. So move the two connections that form the bottom of the inner loop together, joining at a single point. You could even place that connection point on a "stem" connected to the bottom rail of the external circuit. If there's only one path, there's no circuit (closed loop) so no current can flow.

 

[Dethrocutionx]

Thank you so much for the explanation. The help is much appreciated :).