How does this short circuit affect this circuit?

[Vishera]

Homework Statement

Homework Equations

The Attempt at a Solution

I am trying to find the value for i as i→∞. Since ∞>0, I must look at the circuit when t>0. However, when t>0, there is a short circuit. I know that you can short circuit resistors so I can easily short circuit the 3 ohm resistor but what about the 25V voltage source? Isn't short circuiting an ideal voltage source a contradiction because both ends of the voltage source have the same voltage but the entire point of a voltage source is to produce a voltage difference between the two ends?

 

[berkeman]

Homework Statement

Homework Equations

The Attempt at a Solution

I am trying to find the value for i as i→∞. Since ∞>0, I must look at the circuit when t>0. However, when t>0, there is a short circuit. I know that you can short circuit resistors so I can easily short circuit the 3 ohm resistor but what about the 25V voltage source? Isn't short circuiting an ideal voltage source a contradiction because both ends of the voltage source have the same voltage but the entire point of a voltage source is to produce a voltage difference between the two ends?

When that switch closes, it shorts the middle part of the circuit. It does not directly short the 25V source, which would be a bad thing as you say.

Just re-draw the circuit with the switch closed. See how the short basically isolates the left and right sides of the circuit? After the switch is closed, the left and right sides of the circuit operate independently.