Electric Circuits — Cambridge O Level Physics 5054 Revision Notes & Topical Questions

Section 1 of 12Circuit symbols and diagrams

• Circuit diagram
  • a drawing that uses standard symbols to show how components are connected.
• Symbols you need
  • cell, battery, switch, lamp, fixed resistor, variable resistor, fuse, ammeter, voltmeter, thermistor, LDR, diode, LED, relay, transformer, motor,
  • and generator.
  • Components are joined with straight lines for wires, and a dot marks a junction.
• Rules for drawing
  • use a ruler, make a complete loop, and place meters correctly.
• Meters
  • an ammeter goes in series with the component, and a voltmeter goes in parallel with it.
• Conventional current
  • the arrows on a diagram point from the positive terminal around the circuit to the negative terminal.
• Short circuit
  • a low-resistance path that lets a very large current flow, which can overheat wires and cause a fire.

Section 2 of 12Series circuits

• Series circuit
  • the components are connected end to end in a single loop.
• Current
  • the same current flows through every component, I₁ = I₂ = I₃.
• Potential difference
  • the total p.d. is shared between the components, V = V₁ + V₂ + V₃.
  • The p.d. from the supply equals the sum of the p.d.s across each component.
• Resistance
  • the total resistance is the sum, R = R₁ + R₂ + R₃.
    What the symbols mean: R_T = total resistance of resistors in series (Ω) · R₁, R₂ = the separate resistances (Ω)
• Effect of a break
  • if one component fails or a switch opens, the whole circuit stops.
• Cells in series
  • their e.m.f.s add up, so more cells give more energy per coulomb.
• Example
  • a 12 V supply with 4 Ω and 8 Ω in series has R = 12 Ω, I = 1.0 A, and the p.d.s are 4.0 V and 8.0 V.

Section 3 of 12Parallel circuits

• Parallel circuit
  • components are connected on separate branches between the same two points.
• Potential difference
  • it is the same across each branch, equal to the supply voltage.
• Current
  • the total current is shared between branches, I = I₁ + I₂.
  • At a junction, current in equals current out.
• Resistance
  • the combined resistance is smaller than the smallest branch resistor.
  • 1 ÷ R = 1 ÷ R₁ + 1 ÷ R₂,
    • and for two equal resistors R is half of one of them.
      What the symbols mean: R_T = total resistance of resistors in parallel (Ω), always smaller than the smallest one · R₁, R₂ = the separate resistances (Ω)
• Advantages
  • each branch works independently, so a faulty lamp does not stop the others, and each lamp gets the full voltage.
  • This is why household circuits are connected in parallel.

Feature	Series	Parallel
Current	Same everywhere	Splits between branches
p.d.	Shared	Same across each branch
Total resistance	R1 + R2	Less than smallest resistor
If one fails	All stop	Others keep working
Used for	Fairy lights (old types)	Household sockets

Section 4 of 12Solving circuit problems

• Method for mixed circuits
  • reduce the circuit step by step.

1. Find the combined resistance of any parallel parts using the reciprocal formula.
2. Add this to any resistor in series to get the total resistance.
3. Calculate the total current from I = V ÷ R.
4. Use V = IR to find the p.d. across each part.
5. Use the p.d. across each branch to find the branch currents.

• Check
  • the currents in the branches must add to the total, and the p.d.s in series must add to the supply.
• Example
  • 6 Ω and 12 Ω in parallel give 1 ÷ R = 1/6 + 1/12 = 3/12, so R = 4 Ω.

Section 5 of 12Potential dividers and variable resistors

• Variable resistor (rheostat)
  • its resistance can be changed to control the current, for example a dimmer.
• Potential divider
  • two resistors in series across a supply, which split the supply voltage in proportion to their resistances.
• Equation
  • V_out = V_in × R₂ ÷ (R₁ + R₂).
  • V_out is across R₂, so a larger R₂ gives a larger output.
• Using a variable resistor as a potential divider
  • connect the supply across the whole track and take the output between a slider and one end.
  • Moving the slider gives any output voltage from zero up to the supply voltage.
• Applications
  • volume controls, light-sensitive switches and temperature-controlled circuits.

Section 6 of 12Sensors, diodes and switches

• Thermistor (NTC)
  • its resistance decreases as the temperature increases.
  • Used in fire alarms, thermostats and temperature sensing circuits.
• Light-dependent resistor (LDR)
  • its resistance decreases as the light intensity increases.
  • Used in automatic street lights and camera exposure meters.
• Diode
  • it allows current in one direction only (forward) and has a very high resistance in reverse.
  • Used to convert a.c. to d.c. in rectifiers and to protect circuits from reversed connections.
• Light-emitting diode (LED)
  • a diode that gives out light when the current flows forward, and uses much less power than a filament lamp.
  • It needs a protective resistor in series to limit the current.
• Relay
  • an electromagnetic switch that lets a small current switch a large current in a separate circuit.
  • When the coil is energised the iron armature is attracted and closes the contacts of the second circuit.
• Transistor as a switch
  • a small current into the base lets a large current flow from collector to emitter, so it can switch on a lamp or relay.

Section 7 of 12Sensor circuits in practice

• Automatic light
  • an LDR in a potential divider gives a higher voltage in the dark, which is used to switch on a lamp through a transistor.
• Temperature alarm
  • a thermistor in a potential divider gives a changing voltage that triggers a buzzer when the temperature gets too high.
• Choosing the position
  • swapping the sensor and the fixed resistor reverses the effect, so the output rises instead of falls when the input changes.
• Safety circuit
  • a relay lets a low-voltage switch control a mains-powered appliance, keeping the user away from high voltage.

Section 8 of 12Circuit components and symbols in the syllabus

• Sources and meters
  • cell, battery, power supply and generator provide energy, and ammeters and voltmeters measure current and p.d.
• Output devices
  • lamps, heaters, motors and loudspeakers transfer electrical energy to light, heat, movement and sound.
• Control components
  • switches, fixed and variable resistors, fuses and relays control or protect circuits.
• Sensors and diodes
  • thermistors (NTC only), light-dependent resistors, diodes and LEDs respond to the environment or control the current direction.
• Coils and oscilloscope
  • a magnetising coil and a transformer use coils of wire,
  • and an oscilloscope symbol can appear in diagrams to show where a waveform is measured.
• Interpreting a diagram
  • trace the current path from the positive terminal and note which components are in series and which in parallel.

Section 9 of 12Potential divider ratio form

• Ratio of p.d.s
  • for two resistors in series, the p.d.s are shared in the same ratio as the resistances: R₁ ÷ R₂ = V₁ ÷ V₂.
  • A larger resistor takes a larger share of the supply voltage.
• Variable potential divider
  • a variable resistor connected across the supply with the output from the slider gives a smoothly adjustable output between 0 V and the supply voltage.
• Using the ratio
  • if a 6.0 kΩ and 2.0 kΩ resistor share 12 V, then V₁ ÷ V₂ = 3, so the p.d.s are 9.0 V and 3.0 V.
• Sensor input
  • a thermistor or an LDR in a divider turns a change in temperature or light into a change in output voltage.

Section 10 of 12Worked examples

1. Two resistors of 10 Ω and 15 Ω are connected in series across a 15 V supply. Find the current and the p.d. across each. [4]4 marks

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2. A 6.0 Ω and a 3.0 Ω resistor are connected in parallel across 12 V. Find the total current. [4]4 marks

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3. A potential divider has a 4.0 kΩ resistor and a 2.0 kΩ resistor in series across 9.0 V. Find the voltage across the 2.0 kΩ resistor. [3]3 marks

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4. Explain how an LDR can switch on a street light at night. [3]3 marks

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5. Why are lamps in a house connected in parallel? [2]2 marks

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6. Two resistors of 8.0 Ω and 24 Ω are in series across a 12 V supply. Use the ratio method to find the p.d. across each. [3]3 marks

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Section 11 of 12Key terms

Term	Meaning
Series circuit	A circuit with components in one loop sharing the same current.
Parallel circuit	A circuit with components on separate branches sharing the same p.d.
Potential divider	Two resistors in series that split a supply voltage in proportion to their resistances.
Thermistor	A resistor whose resistance changes with temperature, falling as it heats (NTC).
LDR	A light-dependent resistor whose resistance falls as light increases.
Diode	A component that conducts in one direction only.
Relay	A switch operated by an electromagnet that lets a small current control a large one.
Transistor	A component used as a switch or amplifier, controlled by a small base current.

Section 12 of 12Exam technique

1. Adding currents in a series circuit — the same current flows through all series components.
2. Thinking total resistance in parallel is larger — it is always smaller than the smallest branch.
3. Forgetting to take the reciprocal at the end — 1 ÷ R gives 1/R, not R.
4. Placing an ammeter in parallel — it would cause a short circuit, so always use series.
5. Reversing the thermistor behaviour — NTC resistance falls as temperature rises.