this is a solved problem from the textbook i'm using. the results are: v1 = 4.8v, v2 = 2.4v and v3 = -2.4v
the 2ix dependent current source is directed from v3 to ground although v3 is at a lower potential than ground. how is this possible? shouldn't current flow from high potential to low potential?

problem and solution are in attachments.

 

It's a dependent SOURCE.

Draw a simple circuit with a battery and a resistor. Is the current through the battery going from the negative terminal to the positive terminal?

A source has the ability to convert some other form of energy into electrical energy by forcing current to flow from a low potential to a high potential.

It's like saying that rocks have to always fall from a higher elevation (gravitational potential) to a lower gravitational potential. Not true. Put the rocks in an elevator and use some other source of energy to move them upwards against gravity.

 

It's a dependent SOURCE.

Draw a simple circuit with a battery and a resistor. Is the current through the battery going from the negative terminal to the positive terminal?

A source has the ability to convert some other form of energy into electrical energy by forcing current to flow from a low potential to a high potential.

It's like saying that rocks have to always fall from a higher elevation (gravitational potential) to a lower gravitational potential. Not true. Put the rocks in an elevator and use some other source of energy to move them upwards against gravity.

does that happen only with dependent sources?

 

does that happen only with dependent sources?

Notice that I capitalized "source" and not "dependent".

Also noticed that I gave the example of a simple circuit with a battery.