If we open a lot of program and fill up the RAM, does this mean more ram usage equals more power consumption?

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Short answer: no — simply “filling” existing RAM (e.g., 2 GB used versus 3.5 GB used of the same 4 GB stick) does not meaningfully raise the electrical draw of the DIMM. DRAM power is dominated by baseline standby/refresh current and by activity (activations/reads/writes); the number of allocated bytes matters only insofar as it changes how often the memory is accessed. This explains why and were on the right track: the module’s idle/refresh budget is the big component, and ordinary differences in occupancy are negligible compared with active traffic. (micron.com)
Micron — DRAM power tools and notes · “VAMPIRE” DRAM power study (arXiv)

Why there is only a small change: refresh/standby loops are issued by the controller at fixed intervals (and are a non-trivial share of DRAM energy), while the extra energy for reads/writes comes from activation and output drivers — so workloads with lots of memory traffic burn more power even if stored bytes stay the same. Research and vendor notes quantify both the refresh share and the per-access cost. (pmc.ncbi.nlm.nih.gov)
Retention-aware DRAM refresh (PMC) · Micron TN / calculators

Where power can rise in practice: if RAM fills and the OS swaps/pages to disk you’ll see more disk and CPU activity. On systems with spinning HDDs that can be measurable (spindle + actuator draw several watts and spin‑up has a high transient); with NVMe/SATA SSDs the extra power is smaller but still non-zero. That’s the source of ’s intuition about disk activity being the measurable effect. (seagate.com)
Seagate HDD spec examples (idle/active watts) · Crucial rule‑of‑thumb on memory power

Practical tips: avoid swapping (close unnecessary apps or add RAM) if you want to cut system I/O and overall power; prefer SSDs to reduce motor-related draws; enable platform memory power modes (self‑refresh/TCSR) in mobile/BIOS where available; if you need hard numbers, measure system draw with a watt‑meter (Kill‑A‑Watt) while reproducing the workload — the direct RAM occupancy effect will be tiny, but I/O‑heavy swapping is what actually moves the needle. (micron.com)

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You mean more electricity to run the computer? No. You can only install a finite amount of ram in any computer. If you are running so many programs that you fill up all the ram then you have lots of other problems too.

I mean if I fill 2GB out of 4GB of RAM and 3.5GB out of 4GB of RAM, Do they both consume the same amount of power/electricity?

It might consume infinitesimally more because of increased disk activity due to swapping but that would only be because of the stepper motor. That's my guess. Good luck measuring something that small.

It's not likely the electric meter would even notice the difference.

RAM is constantly being refreshed so basically uses constant power. But if you increase the amount of changes in RAM (large quantities of writes) over a given period of time, heat (and electricity usage) will be slightly increased.

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