This is simple experiment I conducted to see effect of capacitor as a charge well/ charge pump to provide current burst in intervals.I had an old cell phone battery and wanted to use it for running my small alarm clock which works on single AA battery. Now a look at datasheet of battery shows capacity of 1100 mAh. I assumed it lasts for 6 months.

So,
\begin{align}6 \, months & = 180 * 24 \, hrs \\ & = 4320 \, hrs \end{align}

which means, clock requires a current of
\begin{align}I&=1100/4320\,mA \\ & = 255 \, \mu A \end{align}

The cell phone battery has voltage of $$3.2V$$. Instead of putting clock in parallel with a voltage divider, I put it in serial with a potentiometer of $$5 k\Omega$$.

Now I turned the pot to find maximum resistance at which clock still runs. It turned out to be $$\approx 1k\Omega$$. But just the resistance with battery would draw $$\approx 3.2mA$$. Which could mean:

1. Clock has huge resistance of $$11.5 k\Omega$$ or,
2. Clock has some lower resistance, but need intermittent current bursts.

Second option above looks more likely since clock involves mechanical movement after each second.

This gives a good opportunity to verify role of capacitor as charge well. So, initially I added a capacitor of $$100 \mu f$$ in parallel with clock. After this addition, clock would run for $$4-5$$ seconds and stop with second hand vibrating in situ.

I thought this might be due to excess capacitance, so replaced the capacitor with $$1 \mu f$$.

Now it started working smoothly. So again I tried to turn the pot till clock stops working. As expected, maximum resistance now increases to $$1.9 k\Omega$$.