My favorite educator, Bill Beaty, often rants at the many misconceptions that all too many people have been infected with.
One of the many common misconceptions involves batteries.
"Frequently-Asked Electricity Questions":
"THE LIQUID BETWEEN A BATTERY'S PLATES IS A GOOD CONDUCTOR.
SO WHY DOESN'T IT SHORT OUT THE BATTERY?"
"Why is electricity so hard to understand?"
"...mistaken belief that no charge flows through batteries. ...
This leads to the traditional incorrect flashlight-current explanation (current comes out of battery, flows...etc.)
It also leads to the misconception that batteries
SUPPLY CHARGE, and have a storage place for "used" charge.
This might make sense if we believe that there's no path for charge through the
battery.
But it's wrong, because there is a path, a path provided by
flowing charged atoms.
Charge must flow around and around a circuit,
passing THROUGH the battery over and over."
"But how SHOULD we teach kids about 'electricity'?"
"A battery is a chemically-fueled charge pump. Like any other pump, a battery takes charges in through one connection and spits them out through the other. A battery is not a source of the "stuff" being pumped. When a battery runs down, it's because its chemical fuel is exhausted, not because any charges have been lost. ...
When you "recharge" a battery, you are pumping charges through it backwards, which reverses the chemical reactions and converts the waste products back again into chemical fuel."
'Which way does the "electricity" really flow?'
"When you connect a lightbulb to a battery, you form a complete circuit, and the path of the flowing charge is through the inside of the battery, as well as through the light bulb filament. Battery electrolyte is very conductive."
it appears to me that the current generated by 35 V and 2vx will
collide each other
It may be that you are assuming that a voltage source, whether independent or controlled, must source current, i.e., supply power to the circuit.
But, at least in ideal circuit theory, there's nothing "wrong" with a voltage source sinking current, i.e., receiving power from the circuit.
For a real world example, consider that, when a battery is being charged, the current is in the opposite direction than when the battery is being discharged.
I would like to know how the current flows across 5 Ω resistor.
If you're planning to be an EE, don't write or say things like "current across"; current is through, voltage is across.
Now, this circuit is very easy to solve. There are two unknowns so you need two independent equations.
For the 1st, write a KVL equation clockwise 'round the loop:
$$35V = v_x + 2v_x - v_o \rightarrow 3v_x = 35V + v_o$$
Now, you need one more independent equation. Can you find one?
Best Answer
For ideal resistors in circuit theory, it's true as soon as the power supply is turned on.
In the real world, no power supply actually turns on instantly. And each resistor has a small parasitic capacitance. And the wires connecting the power supply to the resistors have parasitic indcutance. And each wire has a parasitic capacitance to each other wire in the circuit. If you introduce the effects of these parasitics into your ideal circuit model, you will find that the current does not equalize perfectly through the main wires because some goes through the parasitic capacitors. But this effect is miniscule, due to the non-zero turn-on time of the supply and the wire inductances slow the current turn-on and allow it to stay pretty darn near equal around the loop as it turns on.