Series Circuits

In a series circuit, components are connected one after another in a single loop. There is only one path for current to flow.

Rules for series circuits

Current: The current is the same at every point in a series circuit. There is only one path, so all the charge flows through every component.

$I_{\text{total}} = I_1 = I_2 = I_3$

Potential difference: The total p.d. from the source is shared between the components. The sum of the individual p.d.s equals the e.m.f. of the source.

$V_{\text{total}} = V_1 + V_2 + V_3$

Resistance: The total resistance equals the sum of the individual resistances.

$R_{\text{total}} = R_1 + R_2 + R_3$

Adding more resistors in series increases the total resistance and decreases the current.

Worked example

Three resistors of 10 $\Omega$, 20 $\Omega$ and 30 $\Omega$ are connected in series to a 12 V battery. Calculate the current.

$R_{\text{total}} = 10 + 20 + 30 = 60\text{ }\Omega$

$I = \frac{V}{R} = \frac{12}{60} = 0.20\text{ A}$

The p.d. across the 20 $\Omega$ resistor:

$V = IR = 0.20 \times 20 = 4.0\text{ V}$

Common errors and how to correct them

Saying current is different at each component in series. Current is the same everywhere in a series circuit. It is potential difference that is shared.

Adding p.d.s incorrectly. The p.d.s across the components must add up to the total e.m.f. If they do not, check for a missing component or a calculation error.

How to apply this in an exam

State the rules clearly: same current throughout, p.d.s add up to the supply voltage, total resistance = sum of individual resistances. Show calculations step by step.