Voltage to current calculations

[adrianvon]

Hi all,

With reference to the attached schematic and derivation;
I can understand that Io = Ir2 - Ir3 = Ir1 - Ir3 , but what is the procedure followed for the next 2 steps please?

 

[Ratchit]

What is "R"? Is R3 the unnamed resistor? Are Vi and V1 the same?

Ratch

 

[adrianvon]

Thanks for the reply.

R is referring to the R1/(1+ R2/R3).
As for R3, I think it is referring to the unnamed resistor connected to ground. Also, I think V1 and Vi are referring to the same voltage.

I snapshot I attached was taken from: http://ece.uprm.edu/~mtoledo/5207/S2013/hw1/solhw1.pdf

 

[Ratchit]

Hi all,

With reference to the attached schematic and derivation;
I can understand that Io = Ir2 - Ir3 = Ir1 - Ir3 , but what is the procedure followed for the next 2 steps please?

The voltage at the node of resistor R3 and the LOAD is (vi R2)/R1. Do you understand that? So the current through R3 will be (vi R2)/(R1 R3) . The current io will be Ir1 minus Ir3, not Ir1 plus Ir3 like the answer key says. Therefore, the answer will be vi/R1-(R2/R1 vi) 1/R3 and the R term will have a minus sign in it.

Ratch

 

[Jony130]

Ratch did you forget that the voltage gain for this circuit is negative and this is why we have a plus sign in equation vi/R1 + (R2/R1 vi)*1/R3??

 

[Ratchit]

Ratch did you forget that the voltage gain for this circuit is negative and this is why we have a plus sign in equation vi/R1 + (R2/R1 vi)*1/R3??

Yes, you are correct. Sorry for the mistake. I should have been more careful.

Ratch