Voltage in Series and Parallel
Apply the rules for potential difference in series and parallel circuits and calculate unknown voltages.
Series circuits
In a series circuit the e.m.f. of the supply is shared among the components. The sum of the p.d. across all the components equals the p.d. of the supply:
Vsupply = V1 + V2 + V3
This follows from conservation of energy: each coulomb leaving the cell carries a certain amount of energy, and this is transferred in the components it passes through. If the components are identical, they share the voltage equally; if not, the component with the larger resistance has the larger p.d. across it, because V = IR with the same current in each.
Notice how the series rules connect to the equation V = IR.
Parallel circuits
In a parallel circuit, each branch is connected directly across the same two points, so each branch has the same p.d. as the supply:
V1 = V2 = Vsupply
For this reason, two lamps in parallel across a 6.0 V cell each have 6.0 V across them, however different they are. The lamps in a house are all in parallel so each receives the full 230 V of the mains supply.
Because every branch in parallel sees the full supply voltage, the same lamp shines with the same brightness in a parallel circuit no matter how many other lamps are added, as long as the supply can provide enough current.
Cells and batteries
When cells are connected in series, positive end to negative end, their e.m.f. values add: two 1.5 V cells in series give 3.0 V.
Measuring voltage
Voltmeters are connected in parallel across the component.
When you draw circuits for these questions, label the p.d. across each component with an arrow or a V label. Then check that around any closed loop, the voltage gains from cells equal the voltage drops across components. This rule is the energy conservation law for circuits, and a quick check on your answers.
Potential divider idea
Two resistors in series across a supply divide the supply voltage in proportion to their resistances.
Remember that a switch that is open has the full supply p.d. across it, because no current flows and so there is no p.d. across the other components, whereas a closed switch has zero p.d. across it as its resistance is negligible. This is a useful fault-finding clue: a voltmeter across a broken wire reads the full supply voltage.
Summary table
| Series | Parallel | |
|---|---|---|
| Voltage | Shared; adds to supply voltage | Same across every branch |
| Current | Same | Splits |
Combine this with V = IR to solve circuits with several components.
Worked examples
Worked example 1. Two lamps are in series with a 9.0 V battery. The first has 3.5 V across it. Find the p.d. across the second lamp.
V2 = 9.0 − 3.5 = 5.5 V.
Worked example 2. Three resistors in parallel are connected to a 12 V supply. What is the p.d. across each?
The same as the supply: 12 V across each.
Worked example 3. A 4.0 Ω and a 8.0 Ω resistor are in series with a 6.0 V cell. Find the p.d. across the 8.0 Ω resistor.
I = V/R = 6.0 / 12 = 0.50 A.
V = IR = 0.50 × 8.0 = 4.0 V.
Key terms
| Term | Meaning |
|---|---|
| Potential divider | Series resistors that split a supply voltage. |
| E.m.f. | Energy per coulomb given by a source. |
| Series cells | Cells in a chain whose e.m.f. add. |
| Branch p.d. | Voltage across one branch of a parallel circuit. |