Circuits
Learn H2 Physics resistor networks, I–V curves, internal resistance and potential dividers, then combine capacitors and analyse charging.
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Before you begin
A D.C. circuit shares the energy from a source among its components. The lessons start with reading circuit diagrams and with resistance, resistivity and the I–V characteristics of resistors, lamps, diodes and thermistors. They then allow for the internal resistance of a real source, reduce networks of resistors in series and parallel, and use potential dividers with sensors, before combining capacitors and following them as they charge and discharge through a resistor.
Be comfortable with: currents, because p.d., e.m.f. and electrical power are used throughout.
Learning goals
- Recall circuit symbols and draw or interpret circuit diagrams.
- Draw circuit diagrams containing sources, switches, resistors, meters, lamps, thermistors, light-dependent resistors and diodes.
- Apply resistance and resistivity, interpret I–V characteristics and explain temperature effects.
- Analyse e.m.f., terminal potential difference and internal resistance in real sources.
- Analyse series, parallel and potential-divider resistor networks.
- Combine capacitors in series and parallel.
- Analyse charging and discharging in RC circuits using the time constant.
Syllabus statements covered
- recall and use appropriate circuit symbols
- draw and interpret circuit diagrams containing sources, switches, resistors (fixed and variable), ammeters, voltmeters, lamps, thermistors, light-dependent resistors, diodes, capacitors and any other type of component referred to in the syllabus
- define the resistance of a circuit component as the ratio of the potential difference across the component to the current in it, and solve problems using the equation V = IR
- recall and solve problems using the equation relating resistance to resistivity, length and cross-sectional area, R = ρl/A
- sketch and interpret the I–V characteristics of various electrical components in a d.c. circuit, such as an ohmic resistor, a semiconductor diode, a filament lamp and a negative temperature coefficient (NTC) thermistor
- explain the temperature dependence of the resistivity of typical metals (e.g. in a filament lamp) and semiconductors (e.g. in an NTC thermistor) in terms of the drift velocity and number density of charge carriers respectively
- show an understanding of the effects of the internal resistance of a source of e.m.f. on the terminal potential difference and output power
- solve problems using the formula for the combined resistance of two or more resistors in series
- solve problems using the formula for the combined resistance of two or more resistors in parallel
- solve problems involving series and parallel arrangements of resistors for one source of e.m.f., including potential divider circuits which may involve NTC thermistors and light-dependent resistors
- solve problems using the formulae for the combined capacitance of two or more capacitors in series and in parallel
- describe and represent the variation with time, of quantities like current, charge and potential difference, for a capacitor that is charging or discharging through a resistor, using equations of the form x = x₀e⁻ᵗ⁄τ or x = x₀[1 − e⁻ᵗ⁄τ], where τ = RC is the time constant
Lessons
Work through them in order.
Core lessons
- Circuit symbols and diagramsDraw circuit diagrams with standard symbols and place ammeters and voltmeters correctly.
- Resistance, resistivity and wire geometryDistinguish resistance from resistivity and calculate how wire length and cross-sectional area affect resistance.
- I–V characteristics and temperatureCompare component I–V curves, find resistance at a point and explain metal and semiconductor temperature effects.
- Internal resistance, terminal p.d. and output powerUse V = ε - Ir to explain lost volts and the output power of a real source.
- Resistors in series, parallel and mixed networksIdentify shared nodes and currents, reduce resistor networks and recover individual currents and potential differences.
- Potential dividers with thermistors and LDRsDerive the unloaded divider relationship and choose sensor placement to produce the required output change.
- How a load changes a potential dividerTreat the load as a parallel branch, calculate the changed output and decide when loading is negligible.
- Capacitors in series and parallelDerive and apply the rules for capacitors in series and in parallel from Q = CV.
- Charging, discharging and time constantDescribe capacitor charging and discharging, and use the time constant τ = RC.
Practise and check
Or choose
Topic reference
Quick reference
| Idea | Relation | Notes |
|---|---|---|
| resistance | R = V/I | at the operating point |
| resistivity | R = (ρ l)/A | ρ in Ω m |
| real source | V = ε-Ir | V = ε + Ir while being charged |
| resistors in series | R = R₁ + R₂ + … | same current |
| resistors in parallel | 1/R = 1/R₁ + 1/R₂ + … | same p.d. |
| potential divider | Vₒᵤₜ = VₛR₂/(R₁ + R₂) | no current drawn from the output |
| capacitors in parallel | C = C₁ + C₂ + … | same p.d. |
| capacitors in series | 1/C = 1/C₁ + 1/C₂ + … | same charge |
| RC discharge | x = x₀e^(-t/τ) | charging: x = x₀(1-e^(-t/τ)) for Q and V |
| time constant | τ = RC | 37% left after one time constant |
Core knowledge to remember
- The resistance of a component is the ratio of the potential difference across it to the current in it.
- Ammeters are connected in series; voltmeters in parallel.
- A filament lamp’s resistance rises with temperature because the drift velocity of its electrons falls; an NTC thermistor’s resistance falls because the number density of its charge carriers rises.
- The internal resistance of a source lowers its terminal p.d. as the current rises, and wastes power I²r.
- In a potential divider with a thermistor or LDR, the sensor’s position decides whether the output rises or falls.
- Kirchhoff’s laws, current conservation at a junction and the sum of p.d.s round a loop, are a useful method for networks that cannot be reduced: see Kirchhoff’s first law.
Common mistakes
- Finding the resistance on a curved I–V graph from the tangent instead of V/I.
- Using the diameter for the radius, or millimetres for metres, in R = (ρ l)/A.
- Forgetting the internal resistance when finding the current from a real source.
- Using the resistor combination rules for capacitors.
- Using the unloaded divider equation after a load is connected.
- Thinking a capacitor is fully charged after one time constant.