Series circuits

What a series circuit is

• Components in series are connected one after another in a single loop.
• There is only one path for the charge to follow.
• If one component breaks or is removed, the whole circuit stops — the path is broken.

The three rules

Current is the same everywhere.

$$I_T = I_1 = I_2 = \dots$$

• There is only one path, and charge is conserved, so every coulomb that passes through one component must pass through all the others.
• An ammeter placed anywhere in the loop reads the same value.

Voltages add up to the supply voltage.

$$V_T = V_1 + V_2 + \dots$$

• Each coulomb receives energy in the battery and delivers it to the components in turn, so the energy given out must equal the energy taken in.
• This is conservation of energy applied to each coulomb.

Resistances add.

$$R_T = R_1 + R_2 + \dots$$

• Adding another resistor in series adds another obstruction to the single path, so the total resistance always increases.

How the voltage divides

• The voltages divide in proportion to the resistances.
• The largest resistance gets the largest share of the supply voltage, because the same current flows through all of them and $V = IR$.
• Two equal resistors in series split the supply voltage exactly in half.

Consequences worth knowing

• Adding a component in series increases $R_T$, so from $I = V/R_T$ the current falls everywhere in the circuit.
• Existing bulbs get dimmer when another is added in series, because both the current through them and the voltage across them fall.
• Series is used where components must share a supply voltage, or where a switch must control everything at once — but rarely for lighting, because one failure kills the whole circuit.