I can relate to your question. When I started teaching physics I did not
understand anything beyond formulas. In fact, I did not understand even
formulas correctly. I suspect that this is the case for many physics teachers
in the beginning of their careers.
About your question. Referring to Ohm's law is useful if one starts thinking in
terms of total resistance, potential difference (or voltage) and current (not
just looking at the formula). I use simple circuits with bulbs in series and
parallel. I ask students to rank the bulbs according to brightness. If the
bulbs are identical, brightness is approximately determined by current through
each bulb (there are some complications in a closer analysis because resistance
depends on temperature). Then they (or I) construct the circuit and see what
happens. Any differencies with the prediction will be reconsiled by peer
discussion and with the help from teacher.
"Teaching Introductory Physics" by late Arnold Arons has excellent exercises
and explanations related to simple DC-circuits. I highly recommend this book!
Antti Savinainen
Physics Teacher
Kuopion Lyseo High School/IB
Finland