USAPhO 2015 Problem A2

Consider the circuit shown below. I_{s} is a constant current source, meaning that no matter what device is connected between points \mathrm{A} and \mathrm{B}, the current provided by the constant current source is the same.

a. Connect an ideal voltmeter between A and B. Determine the voltage reading in terms of any or all of R and I_{s}.

b. Connect instead an ideal ammeter between A and B. Determine the current in terms of any or all of R and I_{s}.

c. It turns out that it is possible to replace the above circuit with a new circuit as follows:

From the point of view of any passive resistance that is connected between A and B the circuits are identical. You don’t need to prove this statement, but you do need to find I_{t} and R_{t} in terms of any or all of R and I_{s}.