Circuits & Potential Dividers

Series, parallel, and the elegant logic of potential dividers.

Spec Points Covered
  • State and apply KirchhoffKirchhoff's laws: (1) Conservation of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). at junctions. (2) Conservation of energyThe capacity to do work. Measured in joules (J). around closed loops. Sum of EMFs = sum of IR drops.'s first and second laws.
  • Calculate powerThe rate of energy transfer. Measured in watts (W). using P = IV, $P = I^2R$, and $P = V^2/R$.
  • Calculate total resistanceThe opposition to 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). flow. The ratio of potential difference to 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).. Measured in ohms (Ω). for series and parallel combinations.
  • Derive and apply the potential dividerA circuit that uses two or more resistors in series to produce a fraction of the source voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference. across one of the resistors. equation.
  • Explain how sensor circuits use thermistors and LDRs.
  • Solve multi-step circuit problems combining series and parallel rules.
Notes
01 Conservation of charge Conservation of charge 3.5.1.4 → 02 Electrical power Electrical power 3.5.1.4 → 03 Potential difference Potential difference 3.5.1.4 → 04 Current is the same through each resistor in series $R_{\text{total}} = R_1 + R_2 + R_3$ 3.5.1.4 → 05 P $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$ 3.5.1.4 → 06 Potential divider Potential divider 3.5.1.5 → 07 Potentiometer Potentiometer 3.5.1.5 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
Electrical power (1)
$$P = IV$$
  • Where:
    • $P$ = power (W)
    • $I$ = current (A)
    • $V$ = potential difference (V)
Kirchhoff's first law
$$\sum I_{\text{in}} = \sum I_{\text{out}}$$
  • Where:
    • $I_in$ = current entering a junction (A)
    • $I_out$ = current leaving a junction (A)
Conservation of charge at a junction.
Electrical power (2)
$$P = I^{2}R$$
  • Where:
    • $P$ = power (W)
    • $I$ = current (A)
    • $R$ = resistance (ohm)
Kirchhoff's second law
$$\sum \varepsilon = \sum IR$$
  • Where:
    • $\varepsilon$ = e.m.f. of each source (V)
    • $I$ = current (A)
    • $R$ = resistance of each component (ohm)
Conservation of energy around a closed loop.
Electrical power (3)
$$P = \frac{V^{2}}{R}$$
  • Where:
    • $P$ = power (W)
    • $V$ = potential difference (V)
    • $R$ = resistance (ohm)
Energy transferred
$$E = IVt$$
  • Where:
    • $E$ = energy (J)
    • $I$ = current (A)
    • $V$ = potential difference (V)
    • $t$ = time (s)
Resistors in series
$$R_{\text{total}} = R_1 + R_2 + R_3$$
  • Where:
    • $R_total$ = total resistance (ohm)
    • $R_1, R_2, R_3$ = individual resistances (ohm)
Kilowatt-hour conversion
$$1\;\text{kWh} = 3.6 \times 10^{6}\;\text{J}$$
Resistors in parallel
$$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$
  • Where:
    • $R_total$ = total resistance (ohm)
    • $R_1, R_2, R_3$ = individual resistances (ohm)
Total resistance is always less than the smallest individual resistor. On the AQA data sheet.
Two resistors in parallel (shortcut)
$$R_{\text{total}} = \frac{R_1 \times R_2}{R_1 + R_2}$$
  • Where:
    • $R_total$ = total resistance (ohm)
    • $R_1, R_2$ = individual resistances (ohm)
Product over sum. Only works for exactly two resistors.
Potential divider equation
$$V_{\text{out}} = \frac{R_2}{R_1 + R_2} \, V_{\text{in}}$$
  • Where:
    • $V_out$ = output p.d. across R_2 (V)
    • $V_in$ = supply p.d. (V)
    • $R_1$ = first resistor (ohm)
    • $R_2$ = resistor across which V_out is measured (ohm)
Potential divider ratio
$$\frac{V_1}{V_2} = \frac{R_1}{R_2}$$
  • Where:
    • $V_1$ = p.d. across R_1 (V)
    • $V_2$ = p.d. across R_2 (V)
    • $R_1, R_2$ = series resistances (ohm)
P.d. splits in proportion to resistance.
Q Retrieval Practice All 10 Questions →
Q1. State Kirchhoff's first lawThe sum of currents entering a junction equals the sum of currents leaving. A consequence of conservation of charge. and the conservation law it follows from.
  • At any junction, the total currentThe rate of flow of charge. Measured in amperes (A). entering equals the total current leaving.
  • It follows from the conservation of charge.
Q2. State Kirchhoff's second lawThe sum of EMFs around any closed loop equals the sum of the products of current and resistanceThe opposition to current flow. The ratio of potential difference to current. 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.. and the conservation law it follows from.
  • Around any closed loop, the sum of the e.m.f.s equals the sum of the p.d.s.
  • It follows from the conservation of energyEnergy cannot be created or destroyed, only transferred from one form to another. The total energy of a closed system remains constant..
Q3. Write down three equations for electrical powerThe rate of energy transfer. Measured in watts (W)..
P = IV, P = \(I^{2}\) R, P = \(V^{2}\) / R.
Q4. What is the equation for total resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). of resistors in series?
  • R_total = R_1 + R_2 + R_3.
  • Total resistance is always greater than the largest individual resistor.
Q5. What is the equation for total resistance of resistors in parallel?
  • 1/R_total = 1/R_1 + 1/R_2 + 1/R_3.
  • Total resistance is always less than the smallest individual resistor.