why is more electrical energy consumed by an electric heater per second if the length of its heating element is reduced?

Amount of heat produced per unit time by an electrical heater is given by:

Q = I²R.

 

If the length of the heating element is reduced, R decreases. (since R = ρl/A).

To give the same amount of heating Q, I has to be increased.

 

This increase in I causes a greater consumption of the electrical energy.

(V = IR, R = resistance of supply. V = supply voltage).