luc said:

I have a circuit with 3 resistors.

R1=5500 ohms, R2= 2200 ohms, R3=?

The only other thing that is known is the voltage over R3, which is 4.5V.

How can one derive from this, the current running in this circuit and R3.

What do you have to look for first and why?

First off, if this is a series circuit (as you posted below) then you

are still missing some data. All we can do at this point is lump R1 and R2

and use that as a single 7700 ohm resistor.

So, we have a single known resistance (7700 ohms), a voltage drop across

an unknown resistor (R3), and no idea what the source voltage is. From

that, we can determine only that a) the circuit has at least 7700 ohms of

resistance, b) the supply voltage is at least 4.5 volts, and c) we do not

know enough to figure out anything else.

If R3 is an open circuit, then the supply voltage would indeed be 4.5

volts, and you could not draw more than (4.5V / 7700 ohms) or 584.4

microamps through it. And clearly, R3 cannot be a short or the voltage drop

across it would not be 4.5 volts.

The best you can do is to create a graph showing the relationship

between R3 and the supply voltage, and eliminate many values as being

impossible at either end of the graph. Values of the supply voltage can

only range from 4.5 to infinity at a first approximation.

And, on the resistance axis of the plot, the values of R3 can only range

from some non-zero value to infinity (open circuit). So you have two

definite limits to the graph in any case. Do it on log graph paper, using

sample value of R3 and Ohm's formula to determine the required source

voltage in each test case. The yield will be a curve that will show you for

each assumed value of R3 what the resulting supply voltage will be.

Once you have that value, you can easily determine the current through

the circuit through the formula (Vsupply / (7700+R3)). In fact, just assume

the 7700 ohms as being in series to start with and your graph will yield

your current for any given supply voltage and usable value of R3.

Cheers!

Chip Shults