You are absolutely right. However, that was not my question.
The Var transducer is the same physical device as the Watt transducer. However, to make the Watt tranducer output Vars, there is a phase shift of 90degs applied to the real power hence making it cos(90-angle)=sin(angle), which gives...
A Watt transducer has line to line voltages and line currents as inputs. It calculates the Watts and outputs DC mA. The one i am working on is rated 1mA DC for 500W AC. The relationship is linear.
A Var transducer does exactly the same, but it shifts the input AC by 90degrees to get Vars...