Electrical Circuits

Series, parallel, dividers, and the reality of internal resistance.

Spec Points Covered
  • 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 to any circuit.
  • 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.
  • Explain the effect of connecting cells in series and in parallel.
  • Use 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 to find output 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..
  • Describe how thermistors and LDRs work in sensor circuits.
  • Explain the function of a potentiometerA potential divider with a sliding contact that allows continuous variation of the output voltageThe energy transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference. from zero to the supply voltage..
  • Define EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V)., terminal p.d., and internal resistanceThe opposition to currentThe rate of flow of charge. Measured in amperes (A). flow. The ratio of potential difference to current. Measured in ohms (Ω).The resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). within the source of EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). itself, which causes energy to be dissipated inside the source..
  • Determine EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). and internal resistanceThe resistance within the source of EMF itself, which causes energy to be dissipated inside the source. from a V-I graph.
Notes
01 Kirchhoff's Laws kirchhoff's first law → 02 Series Circuit Rules $V = V_1 + V_2 + V_3 = IR_1 + IR_2 + IR_3$ → 03 Parallel Circuit Rules $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots$ → 04 Cells in Series & Parallel electromotive force → 05 Potential Dividers potential divider → 06 Sensor Circuits (Thermistors & LDRs) → 07 Potentiometers potentiometer → 08 EMF & Internal Resistance internal resistance → 09 Determining EMF and r from a V-I Graph $V = \varepsilon - Ir \quad \Rightarrow \quad \text{gradient} = -r, \quad y\text{-intercept} = \varepsilon$ → 10 Worked Example: EMF & Internal Resistance → 11 Worked Example: Potential Divider with Thermistor → 12 Examiner Command Word Cards →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
Resistors in Series
$$R_{\text{total}} = R_1 + R_2 + R_3 + \ldots$$
  • Where:
    • R in ohms ($\Omega$)
Simply add all resistances. Total is always greater than any individual resistor.
Resistors in Parallel
$$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots$$
  • Where:
    • R in ohms ($\Omega$)
Add reciprocals, then take reciprocal of the result. Total is always less than the smallest resistor. For two resistors: R = R_1 R_2 / (R_1 + R_2). On the OCR data sheet.
Potential Divider Output
$$V_{\text{out}} = \frac{R_2}{R_1 + R_2} \times V_{\text{in}}$$
  • Where:
    • V in volts (V), R in ohms ($\Omega$)
V_out is across R_2. The resistor whose p.d. you want goes in the numerator. Only valid when no current is drawn from the output. On the OCR data sheet.
EMF and Internal Resistance
$$\varepsilon = IR + Ir$$
  • Where:
    • $\varepsilon$ in volts (V), I in amps (A), R and r in ohms ($\Omega$)
EMF = p.d. across external resistance + p.d. across internal resistance. The 'lost volts' are Ir.
Terminal P.D.
$$V = \varepsilon - Ir$$
  • Where:
    • V and $\varepsilon$ in volts (V), I in amps (A), r in ohms ($\Omega$)
Terminal p.d. decreases as current increases. When I = 0, V = EMF. This equation gives a straight-line V-I graph with gradient = -r and y-intercept = EMF.