In the figure below, what is the value ($$kOmega$$) of R needed to make $$i_1=1.25"mA"$$?
We first want to simplify the circuit to find the equivalent resistance ().
Resistors in series add together, so we can add the two 4k resistors together.
Next, we want to get an expression for the combined parallel resistance of and . We can use the equation for finding the equivalent resistance of two resistors in parallel to do so:
Finally, we add this to the 4k resistor in series to find the equivalent resistance of the circuit.
Now that we have the equivalent resistance, we use Ohm's law to solve for R:
Therefore, R must be equal to 8k.