The switch has been opened for a long time. On t=0 the switch is conected. Find the current through R2 for t>=0, the values for R1, R2, R3, E, C are given
​

Hi guys, hope you can help me.

I need to find the current through R2, what are my options?

I think I could say ir2=ic+i1 where ic is the current on the capacitor, which think could find with no problem, nevertheless which would be i1?

Thanks in advance for any help.

 

once the switch is closed, what happens to current through R1? You have a short in parallel with the resistor, so how will that affect the calculations?

I agree that ir2=ic+i1, but what do you think is i1? As far as I know i1 should be the same as the current through R3. Try redrawing, key to these is to redraw with swich closed/open to see how resistors are affected.

 

Thanks for the reply, I think I might have come up with something,

Before the switch is conected

After the switch is conected:

Nevertheless, regardless all of the above; is following statement correct? as the source is always connected to the capacitor (before and after switching), this does not make changes in voltage in the capacitor, which is always charged with the voltage of the source, and, as the voltage in the capacitor equals the voltage R2,

Hence the current on R2 would be:

for all t>=0

 

I tested the circuit on Multisim, and what I stated above does not seem to be true :/

 

this is a tricky one because you have to take into account the fact that capacitor charges up to Vr2 voltage (they are in parallel) when the switch is off. You can use your calculated current to figure out what that voltage is. I bet that third resistor is also 10 ohms. And if you do KVL around loop for i1, you should get a current of 0.6A which you can then use to calculate you t- voltage across capacitor. Once the switch is flipped on, the current changes since resistance is changed.

Vc=Vr2 = E-Vr1-Vr3

hope this makes some sense...

 

The gist of the question, i.e. the part that is of any difficulty to calculate (after you've gotten this far in class) is what the voltage across C will be at t=∞ (or 6-7 RC time constants, whichever is less, usually the time constants when infinity is involved) of switch being open.

Solve for the static voltages as if the switch wasn't there at all, only R1.
Then use those values to re-calculate the activity when R1 is replaced by a wire.

It's not perfectly straightforward, since C isn't connected to either + or GND. It may help re-drawing this with the battery on one side, and all the other components as a column on the other side so it is easy to see what is in series and what is in parallel.