Using more RAM doesn't use more energy. Either your RAM is powered on, or it's not. And if it's powered on it maintains its contents, no matter whether the OS has actually written anything useful to it.
That is not entirely true. Although much of the power dissipation in DRAMs comes from driving the data bus at high speeds (and it happens always, no matter what portion of internal memory space is actually used), some of it comes from memory matrix of the chip. Each DRAM cell is built around tiny on-chip capacitor. The capacitor can be either charged or discharged, which represents two values bit can assume. As bit held in the memory cell toggles its state, the capacitor gets charged and discharged. Whenever the capacitor is charged, it receives a portion of energy from power supply. When it is discharged, that energy is thrown away. The faster the average bit toggle rate and greater the average number of bits toggled, the greater the power dissipation of DRAM. Also, since those capacitors are "leaky" (they discharge spontaneously over time measured in milliseconds), a mechanism is in place to refresh them from time to time. Therefore, if memory contains static data consisting predominantly of bit states which correspond to charged capacitors, it wastes more energy then if it contains predominantly bit states which correspond to empty capacitors.