B.5.11—Conservation in series and parallel circuits

Parallel junctions: conservation of charge

Charge does not accumulate at a steady circuit junction. The total current entering therefore equals the total current leaving:

$$I_{total}=I_1+I_2+\cdots$$

This explains why branch currents add in parallel.

Series path: conservation of energy

Each coulomb receives energy from the source and transfers it through series components. The potential differences across those components therefore add to the supply potential difference:

$$V_{supply}=V_1+V_2+\cdots$$

Use the conservation statements

At a two-branch junction, a missing branch current is $I_2=I_{total}-I_1$. In local practice question 4, the series supply is $12\,\mathrm V$ and the lamp drop is $4.0\,\mathrm V$, so the other series component has $V=12-4.0=8.0\,\mathrm V$.

Boundary

These are the simple series/parallel consequences required here. Do not extend this card to arbitrary multi-loop equation solving.