Ac current source(1-10mA) with help of 5V dc battery
It depends on your design specs and depends on output ESR of Op Amp which limtis the load regulation error of your Howland CC sink due to the Value of feedback R's

(Ballpark) I would expect CMOS Howland CC has a 2mA limit gives you 10% load regulation and &lt;&lt; 1mA gives you almost perfect CC even if device specifies short circuit current much higher. 

BJT 5V Op Amps will improve Icc limit, if you can satisfy the CM input range and Vout drop to rails.

Here is my poor example with an ideal OA degraded with an example of  CMOS OA 1k open loop output resistance for 1.5mA CC. Then see how current changes when you push switch.  BJT types may be towards 300 Ohms. Read specs carefully for Vol/Iol.

You can improve this by careful selection of OA with critical input&lt;>output specs.