How to build a voltage-controlled current sink / voltage-controlled resistor
This is a voltage controlled current sink that has a LED as its load but anything as a load would do: -



Like I say - ignore the LED and assume it's just a resistor up to some abitrary positive supply voltage that needn't be the same as the op-amp.

It works by ensuring the voltage across the emitter resistor is the same as the voltage on the potential divider on the +Vin of the op-amp - the op-amp controls the BJT to make sure that 1V is across the 10 ohm resistor thus 100mA will always flow through the LED/Load in the collector.

If you want a smaller current either make the potential divider produce a smaller voltage on the +Vin of the op-amp or increase the 10R emitter resistor. Here's a similar circuit that controls a current source referenced to the +V rail: -



This circuit uses FETs instead of a BJT just to demonstrate the possibilities. The op-amp and FET to the left control the current through a 1k resistor to +Vs. There's a cap across it to stabilize the voltage across the 1k to prevent FET leakage capacitance making it noisy.

The voltage across this 1k is therefore identical to Vin (use low Vos op-amps and it will be within a hundred uV. The 2nd part of the circuit take the +Vs referenced voltage and creates a constant current source for the load. In this circuit the current through the load is Vin/100.

Making a voltage controlled resistance is much much harder to achieve linearity but if that's the way to go good luck.