10.1 Practical circuits
- Syllabus
- 9702–2028–2029
- Topic
- 10.1
- Level
- AS
Learning objectives
10.1.1The circuit symbols shown in section 6 of this syllabus• recall and use the circuit symbols shown in section 6 of this syllabus10.1.2Draw and interpret circuit diagrams containing the circuit symbols shown in• draw and interpret circuit diagrams containing the circuit symbols shown in section 6 of this syllabus10.1.3The electromotive force (e.m.f.) of a source as energy transferred per unit• define and use the electromotive force (e.m.f.) of a source as energy transferred per unit charge in driving charge around a complete circuit10.1.4E.m.f. and potential difference (p.d.) in terms of energy considerations• distinguish between e.m.f. and potential difference (p.d.) in terms of energy considerations10.1.5The effects of the internal resistance of a source of e.m.f. on the terminal• understand the effects of the internal resistance of a source of e.m.f. on the terminal potential difference
Recognise the complete Cambridge circuit-symbol set
| Group | Official symbols and discriminating cues |
|---|---|
| sources | cell: one long/short parallel-line pair; battery of cells: repeated pairs; power supply: two terminals; a.c. power supply: two terminals with ~ |
| connections | junction of conductors: connected wires with a filled dot; switch: two contacts with a movable open/closed link; earth: vertical connection to three decreasing horizontal bars |
| Group | Official symbols and discriminating cues |
|---|---|
| resistive/light | lamp: circle with cross; fixed resistor: rectangle; variable resistor: rectangle with diagonal arrow; heater: segmented rectangle |
| sensors/control | thermistor: resistor with diagonal temperature mark; LDR: resistor with arrows pointing towards it; potentiometer: three-terminal resistor with sliding contact |
| semiconductor/storage | diode: one-direction diode mark with barrier; LED: diode plus two arrows pointing outwards; capacitor: two parallel plates |
| Group | Official symbols and discriminating cues |
|---|---|
| sound | electric bell and buzzer use opposite dome/bowl cues; microphone has a receiving diaphragm; loudspeaker has an outward cone |
| machines | motor: circle marked M; generator: box marked G |
| meters/display | ammeter: circle A; voltmeter: circle V; galvanometer: circle with pointer; oscilloscope: circle with trace |
Use the exact symbol, orientation and number of terminals required. The long cell line is the positive terminal. Arrows pointing towards an LDR represent incoming light; arrows pointing away from a diode identify an LED. A filled dot means joined conductors; crossing lines without a junction mark are not automatically connected.
Component names are not substitutes for symbols in a requested circuit diagram. Reversing a cell, diode or LED, changing a sliding contact, or adding/removing a junction changes the electrical meaning.
Draw and read circuits from their topology
To draw a circuit: list the required components and measurements; identify which components share one current path and which form branches; place standard symbols with correct polarity/orientation; connect straight wires and mark only true junctions; then label values and check a complete path between supply terminals.
| Measurement | Connection | Why |
|---|---|---|
| current through a component | ammeter in series in that branch | the same branch current passes through the meter |
| p.d. across a component | voltmeter in parallel across its two terminals | the meter compares those two potentials |
To interpret a diagram, ignore where components are drawn on the page and trace electrical nodes instead. Points joined by ideal wire belong to the same node. Components connected between the same two nodes are parallel; components on an unbranched path are series. Then check switch state, source polarity and diode direction before predicting current.
For a nichrome-wire investigation, draw the wire as a resistor in a closed loop with the cell and ammeter in series, and connect a voltmeter across only the wire. This measures the wire's I and V without including the ammeter's p.d. in the voltmeter reading.
A voltmeter in series can almost break the circuit because of its high resistance; an ammeter across a supply can cause a dangerously large current because of its low resistance. A line crossing is not a junction unless the diagram marks a connection.
E.m.f. is source energy supplied per coulomb around the complete circuit
The electromotive force ε of a source is the energy transferred by the source per unit charge in driving charge around the complete circuit. It converts chemical, mechanical or another stored form into electrical energy.
ε=W/QandW=εQ
ε is measured in volts, with 1 V = 1 J C⁻¹. W is the total source energy supplied to the complete circuit, including energy transferred in the external circuit and any internal resistance.
A 9.0 V battery drives 250 C around its circuit. The energy converted by the battery is W = εQ = 9.0 × 250 = 2.25 × 10³ J. If internal resistance is present, not all of this reaches the external load.
E.m.f. is not a force in newtons. It characterises the source's energy conversion per coulomb and can remain constant even while loaded terminal p.d. changes.
E.m.f. supplies energy; p.d. transfers it from electrical form
| Feature | E.m.f. ε of a source | Potential difference V across a component |
|---|---|---|
| meaning | energy supplied by source per unit charge | energy transferred from electrical form per unit charge |
| energy conversion | chemical/mechanical/etc. → electrical | electrical → thermal/mechanical/light/etc. |
| location | across the source's energy-raising process | between the two terminals of the named component |
| unit | V = J C⁻¹ | V = J C⁻¹ |
For each coulomb around a complete steady circuit, energy supplied by the source equals the sum of energy transferred per coulomb in external components and inside the source. Thus ε equals the sum of all p.d. drops around the loop.
A 1.5 V cell supplies 1.5 J C⁻¹. If 0.20 J C⁻¹ is transferred internally, the terminal p.d. available to the external circuit is 1.3 V; the two numbers describe different energy destinations.
Equal numerical values do not make e.m.f. and p.d. the same process. With zero current, internal transfer is negligible and terminal p.d. approaches ε; under load, internal loss can make terminal p.d. smaller.
Internal resistance makes terminal p.d. depend on current
ε=V+IrsoV=ε−Ir
A real source is modelled as e.m.f. ε in series with internal resistance r. When current I is delivered, Ir is the p.d. lost inside the source and I²r is the internal power dissipation; the terminal p.d. V is what remains for the external circuit.
Decreasing external resistance increases total current. The internal drop Ir then increases, so terminal p.d. falls even if ε is unchanged. Increasing external resistance does the reverse. With an ideal high-resistance voltmeter and open circuit, I ≈ 0 and V ≈ ε.
For ε = 6.0 V, r = 0.50 Ω and I = 2.0 A, V = 6.0 − (2.0)(0.50) = 5.0 V. Internal power is I²r = 2.0 W, while power delivered at the terminals is VI = 10 W.
A graph of terminal V against delivered I is a straight line V = ε − rI: the V-axis intercept is ε and the gradient is −r. A lower ε moves the intercept down; a lower r makes the line less steep.
Internal resistance is part of the source model, not an added external resistor. Current changes terminal p.d. through internal energy transfer; it does not necessarily change the source e.m.f.