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 12Circuit 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 |
Circuit symbols and component functions
All symbols
- All symbols every symbol on the syllabus list, including the less common ones, must be recognised and drawn.
Reading a diagram
- 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 12Electromotive force (e.m.f.)
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
- Measurement use a high-resistance voltmeter across the cell terminals in an open circuit.
Potential difference
Potential difference the energy transferred from each coulomb as it passes through a component, p.d. = energy transferred ÷ charge.
Difference
- 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.
- Voltage and p.d. they mean the same thing, but neither should be confused with e.m.f.
Section 3 of 12Internal resistance and lost volts
Internal resistance r
- 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
- Model a cell is an ideal source of e.m.f. in series with its internal resistance.
Terminal p.d.
- 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)
Lost volts
- 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 12Kirchhoff's first law
1Statement
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.
2Junction and branch
- Junction and branch a junction is where three or more paths meet and a branch joins two junctions.
3Series
- Series the current is the same everywhere.
4Parallel
- Parallel the current divides at each junction, and the law applies at every junction.
5Method
- Method mark arrows for conventional current at each junction to see which currents enter and which leave.
Section 5 of 12Kirchhoff's second law
Statement
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
- Series circuit the e.m.f. is shared between components in proportion to their resistance.
Parallel circuit
- Parallel circuit each closed loop acts as its own series circuit, so each branch has the same p.d. as the supply.
Household wiring
- 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 12Resistors in series and parallel
Series
- Series the current is the same through every resistor, and the p.d. is shared, so R = R1 + R2 + R3 + …
- DerivationV = 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
- 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
- Reciprocals after adding the reciprocals, take the reciprocal again (x−1 button) to obtain R.
Section 7 of 12Solving problems with the laws
1
Mark the direction of conventional current on every branch.
2At each junction apply the first law
At each junction apply the first law current in
current out.
current out.
3Around each loop apply the second law
Around each loop apply the second law total e.m.f.
sum of the p.d. values.
sum of the p.d. values.
4Use V
IR to link p.d., current and resistance, then solve for the unknown.
Solving problems with the laws
Identical components in series
- Identical components in series they carry the same current, so they have equal p.d. values.
Ammeters
- 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.
Section 8 of 12Potential dividers
Potential divider
Potential divider two or more resistors in series across a supply, giving an output voltage that is a fraction of the input.
- Usesprovide a variable p.d., choose a particular p.d. or split a supply p.d. between components.
Equation
- Vout = [R2 ÷ (R1 + R2)] × Vin.
- R2 in the numerator is always the resistance across which Vout is measured.
Share
- Share 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 12Potentiometer and galvanometer
Potentiometer
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
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
- 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.
- 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
- Wire length p.d. is proportional to length of wire, so a longer length gives a higher p.d.
Section 10 of 12Sensor potential dividers
LDR divider
- 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
- Thermistor divider its resistance falls as temperature rises;
- used in fire alarms, ovens and digital thermometers.
Behaviour
- 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
- Switching the output can switch a device on or off, such as a heater turning off at room temperature.
Section 11 of 12Key terms
| Term | Meaning |
|---|---|
| E.m.f. | Energy transferred to each coulomb of charge by a power source. |
| Potential difference | Energy transferred from each coulomb of charge as it passes through a component. |
| Internal resistance | The resistance inside a power supply that wastes some energy as heat. |
| Lost volts | The voltage Ir dropped across the internal resistance. |
| Kirchhoff's first law | Current into a junction equals current out, from conservation of charge. |
| Kirchhoff's second law | The e.m.f. in a loop equals the sum of the p.d. values, from conservation of energy. |
| Potential divider | Resistors in series giving an output voltage that is a fraction of the input. |
| Potentiometer | A variable resistor used as a potential divider with a sliding contact. |
| Galvanometer | A sensitive ammeter used to detect zero current in null methods. |
Section 12 of 12Exam technique
1
Treating the terminal p.d. as the e.m.f. when current flows — the terminal p.d. is E − Ir.
2
Leaving the parallel answer as 1/R — invert again to find R.
3
Putting the wrong resistor in the numerator of the divider equation — use the resistance Vout is measured across.
4
Connecting an ammeter in parallel or a voltmeter in series — ammeters go in series, voltmeters in parallel.
5
Saying p.d. is shared equally in series — it is shared in proportion to resistance.