Node Voltage Method in Circuit Analysis

[Noesis]

I really don't understand exactly how they got the term highlighted in yellow.

We want to get all values for all of the currents coming into or out of the node...so why does it have what appears to be the voltage across the 1 ohm resistor divided by the equivalent resistance of the 1 ohm and 4 ohm?

Wouldn't the current out that branch be vo/5 anyway?

Someone please help.

Thank you guys.

 

[marcusl]

No, the current in that branch is (v0-45)/5 as they have written. Conceptually you can move the 1 ohm resistor down to the position of the 4 ohm, making it 5 ohms instead. That might make it clear to you that the voltage across the 5 ohm resistor is v0-45.

 

[Noesis]

Thanks for the reply Marcus!

Why? That doesn't make much sense really.

How can just moving a resistor 'over' a battery produce an equivalent circuit?

 

[ranger]

It does not matter the position of the 4 ohm resistor; whether its on the wire that connects to the negative end of the battery or the positive. What matters here is that the same amount of current will flow though both. In other words, both of these resistors will control the current flow. Leave the circuit as is and just trace the total current coming out from one terminal of the battery, you will find that the same amount flows through both resistors.

Wouldn't the current out that branch be vo/5 anyway?

But we have 45V source on one end and vo on the other; neither of which are 0V. Voltage is the difference of electrical potential between two points.

 

[Noesis]

Thank you very much Ranger.

I couldn't have understood it without your reply. Realizing what to do with the 45V source was crucial.