Constant Current Source Circuit Analysis · USAPhO 2015 #A2
Physics · electromagnetism
Problem
Consider the circuit shown below. Is is a constant current source, meaning that no matter what device is connected between points A and B, the current provided by the constant current source is the same.
[Figure: Circuit diagram showing a constant current source Is with resistors arranged in parallel paths between points A and B. Top path: 4R in series with 2R. Bottom path: 2R in series with 4R. A middle resistor of 2R connects between the junction points of the top and bottom paths.]
a. Connect an ideal voltmeter between A and B. Determine the voltage reading in terms of any or all of R and Is.
b. Connect instead an ideal ammeter between A and B. Determine the current in terms of any or all of R and Is.
c. It turns out that it is possible to replace the above circuit with a new circuit as follows:
[Figure: Simple equivalent circuit with current source It in parallel with resistance Rt between points A and B]
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 It and Rt in terms of any or all of R and Is.