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D.C. Circuits

10. D.C. Circuits

10 min read 10 parts Lesson 1 of 1

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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

Part 1 of 10Circuit symbols and component functions

ComponentFunction
SwitchClosed turns the circuit on, open turns it off
Fixed resistorLimits current; its resistance cannot be changed
Variable resistorHas a slider to change resistance, used in dimmers and volume controls
ThermistorResistance falls as temperature rises and rises as temperature falls
Light-dependent resistor (LDR)Resistance falls as light intensity rises
DiodeLets 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
AmmeterMeasures current; connected in series
VoltmeterMeasures 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.

Part 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.

Part 3 of 10Internal resistance and lost volts

1Internal resistance r1 point
— 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.
2Model
— a cell is an ideal source of e.m.f. in series with its internal resistance.
3Terminal 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)
4Lost volts1 point
— the voltage Ir dropped across the internal resistance, not available to the circuit.
  • Lost volts = e.m.f. − terminal p.d.
QuantityEquation
E.m.f.E = IR + Ir = I(R + r)
Terminal p.d.V = E − Ir
Lost voltsIr
  • Current effect — as current increases, lost volts increase and terminal p.d. falls.

Part 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.

Part 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.

Part 6 of 10Resistors in series and parallel

1Series2 points
— 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.
2Parallel2 points
— 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.
3Reciprocals
— after adding the reciprocals, take the reciprocal again (x−1 button) to obtain R.

Part 7 of 10Solving problems with the laws

  1. Mark the direction of conventional current on every branch.
  2. At each junction apply the first law: current in current out.
  3. Around each loop apply the second law: total e.m.f. sum of the p.d. values.
  4. 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.

Part 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.
2Equation1 point
— Vout = [R2 ÷ (R1 + R2)] × Vin.
  • R2 in the numerator is always the resistance across which Vout is measured.
3Share1 point
— 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.

Part 9 of 10Potentiometer and galvanometer

1Potentiometer2 points
= 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).
2Galvanometer1 point
= 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.
3Null deflection
— the pointer sits at zero when there is no current, so the p.d. across the galvanometer is zero.
4Comparing e.m.f.2 points
— 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.
5Wire length
— p.d. is proportional to length of wire, so a longer length gives a higher p.d.

Part 10 of 10Sensor potential dividers

  • LDR dividerthe LDR's resistance falls as light increases, so its share of the p.d. falls; used in street and security lights.
  • Thermistor dividerits resistance falls as temperature rises; used in fire alarms, ovens and digital thermometers.
  • Behaviourthe 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.
  • Switchingthe output can switch a device on or off, such as a heater turning off at room temperature.

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