3.5.1.4
Potential difference
Circuits & Potential Dividers — AQA A-Level Physics
Key Definition
Potential difference — The energy transferred per coulomb of charge flowing between two points. Measured in volts (V).
$$V = \frac{W}{Q}$$
- If chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). carriers lose energyThe capacity to do work. Measured in joules (J)., the p.d. is a potential dropA decrease in electric potential across a component as energy is transferred from charge carriers to the component..
- If chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). carriers gain energyThe capacity to do work. Measured in joules (J)., the p.d. is a potential riseAn increase in electric potential, typically across a source of e.m.f. such as a battery..
- A cell provides a potential rise. A resistor causes a potential drop.
Key Definition
Kirchhoff's second law — Around any closed loop in a circuit, the sum of the e.m.f.s equals the sum of the p.d.s. This is a consequence of conservation of energyEnergy cannot be created or destroyed, only transferred from one form to another. The total energy of a closed system remains constant..
$$\sum \varepsilon = \sum IR$$
- For components in seriesComponents connected end-to-end in a single path, so current flows through each in turn.: $total p.d. = sum of individual p.d.s.$
- For components in parallelComponents connected across the same two points, providing multiple current paths.: p.d. across each branch is the same.
$$V_{\text{total}} = V_1 + V_2 + V_3 \quad \text{(series)}$$
$$\begin{aligned}
V_{\text{total}} &= V_1 \\
&= V_2 \\
&= V_3 \quad \text{(parallel)}
\end{aligned}$$
Series and parallel PD diagrams
Two side-by-side circuit diagrams: (1) three resistors in series with V_total = V_1 + V_2 + V_3, (2) two resistors in parallel with V shared across both branches.
Examiner Tips and Tricks
- When applying Kirchhoff's second lawThe sum of EMFs around any closed loop equals the sum of the products of currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). and resistanceThe opposition to currentThe rate of flow of charge. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of charge. Measured in amperes (A).. Measured in ohms (Ω). (IR). A consequence of conservation of energyThe capacity to do work. Measured in joules (J).Energy cannot be created or destroyed, only transferred from one form to another. The total energy of a closed system remains constant.., choose a loop direction and be consistent.
- A p.d. across a resistor is negative if current flows in the opposite direction to your chosen loop.
Common Mistake
MEDIUM
Students often: Confusing KirchhoffKirchhoff's laws: (1) Conservation of charge at junctions. (2) Conservation of energy around closed loops. Sum of EMFs = sum of IR drops.'s first and second laws.
Instead: First law = junctions = charge conservation. Second law = loops = energy conservation. Think: 'First, charge arrives at the Junction. Second, energy goes around the Loop.'
Instead: First law = junctions = charge conservation. Second law = loops = energy conservation. Think: 'First, charge arrives at the Junction. Second, energy goes around the Loop.'