Loops in parallel circuits

Separate loops are the key to unlocking parallel circuits

Circuits with only one parallel connection are best analysed by thinking of the two separate loops that make up the circuit. The introduction to parallel connections in circuits was made in this way in the SPT: Electric circuits topic. The loops have nothing in common, other than the battery, so you can treat them as two separate loops.

Then simply use the relationship

I = VR

for each loop to find the current in each. The potential difference and the resistance in the loop together set the current in each loop. The current in the battery is the sum of the current in each of the loops, as the battery is in both loops. The interactive keeps things very simple because the two arms of the parallel circuit are identical.

You can model this process rather effectively using a modelling package, to show on a single screen all of the calculations that you perform and the relationships between the different currents, resistances and the potential difference. Here you can easily vary the resistance of the two loops independently.