I am working with 3VDC at 10mA that I want to use to turn on a relay with; so far I can’t find a relay that will work at that voltage and low current. I do have a 3VDC relay but it needs 60mA to turn on.
So I would like to know if there is a way to amplify the amperage from 10mA to 60mA, if so what will I need?
3V * 10mA = 30mW of power that you have at your disposal ..
In theory you can generate 60mA out of 30mW but the output voltage (assuming 100% efficiency) will be 30mW/60mA = 0.5V ..
So, as you can see, any micro-power relay is out of question ..
However, 3V and 10mA can be used to drive an optocoupler and the other side of an optocoupler, which can be a transistor, or a triac can be used to switch bigger loads ..
I think an optocoupler will be ideal for your application and switching 8mA at 5V can be done by easily done by common and inexpensive units .. see picture below ..
You shouldn't have much trouble .. optcouplers are readily available ..
As in most cases the forward volage accross the "primary" diode is 1.5V, don't forget to connect ≈220-300Ω resistor in series with it ..