Equivalent Resistance

This circuit produces an output voltage, Vo, that is proportional to the input current, Is. The output voltage is measured using a voltmeter. The input current is the current of the current source. The constant of proportionality is called the equivalent resistance of the circuit consisting of R1, R2 and R3. The value of the equivalent resistance is determined by the values of R1, R2 and R3.

First, R1 is in series with R2. The series resistors are connected in parallel with R3. The equivalent resistance, Req, is given by

Notice that when Is = 1, Req = Vo. (The equivalent resistance is "numerically equal" to the output voltage but they have different units.)

Suppose a value of Req is specified. There is no guarantee that values of R1, R2 and R3 can be found to produce the specified ver of equivalent resistance. Let's start be choosing R1 and R2 so that

Next choose R3 so that