Electricity and D.C. circuits
10. D.C. Circuits — Cambridge AS & A Level Physics 9702 Revision Notes & Topical Questions
5 min read 10 parts Lesson 26 of 26 Unit quiz
Lesson summary
Circuits — Cambridge AS & A Level Physics 9702 — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Use circuit symbols, e.m.f. and internal resistance, Kirchhoff's laws, series and parallel resistance, and potential dividers to analyse d.c.
- 10. D.C. Circuits — Cambridge AS & A Level Physics 9702 — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes
- All symbols
- Reading a diagram
- Measurement
- Potential difference
- Voltage and p.d
Section 1 of 10Circuit symbols and component functions
| Component | Function |
|---|---|
| Switch | Closed turns the circuit on, open turns it off |
| Fixed resistor | Limits current; its resistance cannot be changed |
| Variable resistor | Has a slider to change resistance, used in dimmers and volume controls |
| Thermistor | Resistance falls as temperature rises and rises as temperature falls |
| Light-dependent resistor (LDR) | Resistance falls as light intensity rises |
| Diode | Lets current pass in one direction only; used to change a.c. to d.c. |
| Light-emitting diode (LED) | A diode that emits light when current flows; used in aviation lighting and displays |
| Ammeter | Measures current; connected in series |
| Voltmeter | Measures potential difference; connected in parallel |
- All symbols
- every symbol on the syllabus list, including the less common ones, must be recognised and drawn.
- Reading a diagram
- a circuit conducts only if the switch is closed and any diode points in the direction of conventional current.
Section 2 of 10Electromotive force (e.m.f.)
- E.m.f. = the energy transferred to each coulomb of charge by a power supply, e.m.f. = energy transferred ÷ charge, measured in volts.
- It measures the energy the source puts into the circuit.
- It equals the terminal p.d. when no current flows.
- Measurement
- use a high-resistance voltmeter across the cell terminals in an open circuit.
- Potential difference = the energy transferred from each coulomb as it passes through a component, p.d. = energy transferred ÷ charge.
- Difference
- e.m.f. is energy supplied to the charge, while p.d. is energy taken from the charge by components.
- Voltage and p.d.
- they mean the same thing, but neither should be confused with e.m.f.
Section 3 of 10Internal resistance and lost volts
- Internal resistance r
- every real supply has resistance between its terminals, which wastes energy as heat inside the cell.
- This is why a cell warms up when it supplies current.
- Model
- a cell is an ideal source of e.m.f. in series with its internal resistance.
- Terminal p.d.
- the voltage available to the external circuit, V = IR.What the symbols mean: V = potential difference (V) · I = current (A) · R = resistance (Ω)
- the voltage available to the external circuit, V = IR.
- Lost volts
- the voltage Ir dropped across the internal resistance, not available to the circuit.
- Lost volts = e.m.f. − terminal p.d.
| Quantity | Equation |
|---|---|
| E.m.f. | E = IR + Ir = I(R + r) |
| Terminal p.d. | V = E − Ir |
| Lost volts | Ir |
- Current effect
- as current increases, lost volts increase and terminal p.d. falls.
Section 4 of 10Kirchhoff's first law
- Statement = the sum of the currents entering a junction equals the sum of the currents leaving it.
- It follows from conservation of charge, because charge cannot build up at a point.
- Junction and branch
- a junction is where three or more paths meet and a branch joins two junctions.
- Series
- the current is the same everywhere.
- Parallel
- the current divides at each junction, and the law applies at every junction.
- Method
- mark arrows for conventional current at each junction to see which currents enter and which leave.
Section 5 of 10Kirchhoff's second law
- Statement = in a closed loop, the total e.m.f. equals the sum of the potential differences across the components.
- It follows from conservation of energy.
- Series circuit
- the e.m.f. is shared between components in proportion to their resistance.
- Parallel circuit
- each closed loop acts as its own series circuit, so each branch has the same p.d. as the supply.
- Household wiring
- appliances are in parallel so each gets the full supply p.d. and the rest keep working if one fails.
Section 6 of 10Resistors in series and parallel
- Series
- the current is the same through every resistor, and the p.d. is shared, so R = R1 + R2 + R3 + …
- Derivation: V = V1 + V2 + … by the second law, and dividing by the common current I gives the sum.
- The combined resistance is larger than any single resistor.
- Parallel
- the p.d. is the same across every resistor, and the current splits, so 1/R = 1/R1 + 1/R2 + 1/R3 + …
- Derivation: I = I1 + I2 + … by the first law, and dividing by the common p.d. V gives the sum of reciprocals.
- The combined resistance is smaller than the smallest resistor, and two equal resistors in parallel give half of one.
- Reciprocals
- after adding the reciprocals, take the reciprocal again (x−1 button) to obtain R.
Section 7 of 10Solving problems with the laws
- Mark the direction of conventional current on every branch.
- At each junction apply the first law: current in current out.
- Around each loop apply the second law: total e.m.f. sum of the p.d. values.
- Use V IR to link p.d., current and resistance, then solve for the unknown.
- Identical components in series
- they carry the same current, so they have equal p.d. values.
- Ammeters
- an ammeter in series with a component reads that component's current,
- and a branch ammeter reads the difference between the main current and the other branches.
- an ammeter in series with a component reads that component's current,
Section 8 of 10Potential dividers
1Potential divider1 point
= two or more resistors in series across a supply, giving an output voltage that is a fraction of the input.
- Uses: provide a variable p.d., choose a particular p.d. or split a supply p.d. between components.
2Equation2 points
- Vout = [R2 ÷ (R1 + R2)] × Vin.
- R2 in the numerator is always the resistance across which Vout is measured.
3Share2 points
- the resistor with the larger resistance has the larger p.d., because V = IR with the same current.
- Increasing one resistance increases its share and reduces the other's share.
Section 9 of 10Potentiometer and galvanometer
- Potentiometer = a variable resistor used as a potential divider with a slider (arrow) that gives a continuously variable output.
- Moving the slider changes the resistances, and so the p.d., of the upper and lower parts.
- The output ranges from a maximum (full track in the output part) to a minimum (none of the track, or only a fixed resistor).
- Galvanometer = a very sensitive ammeter, a circle with an arrow, used to detect small currents.
- It has a coil of wire on an iron core rotating in a magnetic field.
- Null deflection
- the pointer sits at zero when there is no current, so the p.d. across the galvanometer is zero.
- Comparing e.m.f.
- a cell of e.m.f.
- E2 is connected through the galvanometer to the wire, with its polarity opposing the driver cell.
- The slider is moved until the galvanometer reads zero.
- The p.d. along the wire section then equals E2 and the two oppose, so no current flows.
- Wire length
- p.d. is proportional to length of wire, so a longer length gives a higher p.d.
Section 10 of 10Sensor potential dividers
- LDR divider
- the LDR's resistance falls as light increases, so its share of the p.d. falls; used in street and security lights.
- Thermistor divider
- its resistance falls as temperature rises; used in fire alarms, ovens and digital thermometers.
- Behaviour
- the current is common, so a rise in a component's resistance raises its p.d., and the other component's p.d. falls because the total equals Vin.
- Switching
- the output can switch a device on or off, such as a heater turning off at room temperature.
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