10.15-10.16 - Series calculations and measurement circuits

Calculate series-circuit quantities

In a series circuit, components form one unbranched loop. Charge has only one route, so the current is the same through every component. The source transfers energy to each coulomb of charge; the potential differences across the components show how that energy is shared.

For resistors in series:

• the current is the same at every point;
• the potential differences across the components add to the supply potential difference;
• the total resistance is the sum of the individual resistances.

Current is not used up as it passes through a resistor. The same charge per second reaches every point in the loop. What changes across a resistor is the energy transferred per coulomb, represented by the potential difference.

Worked example. A 12 $\Omega$ resistor and an 18 $\Omega$ resistor are connected in series across a 9.0 V supply. Calculate the circuit current and the potential difference across each resistor.

First add the series resistances:

Then rearrange $V=IR$ for the whole circuit:

The same 0.30 A passes through both resistors, so:

The checks agree with the model: $3.6+5.4=9.0\text{ V}$, and the larger resistance has the larger share of the supply potential difference.