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Circuit symbols and Kirchhoff's laws

Kirchhoff's first law is conservation of charge at a junction and his second law is conservation of energy around a closed loop. Before either come the standard circuit symbols, with the ammeter placed in series and the voltmeter across the component it measures. Current is not used up on the way round; energy is what a component takes.

Circuit symbols and Kirchhoff's laws

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Year 12AQA 3.5.1.4CIE 10.1.1, 10.1.2, 10.2.1, 10.2.2OCR A 4.1.1(g), 4.2.1(a), 4.2.1(b), 4.3.1(a), 4.3.1(b)EDEXCEL 34, 35

Circuits and Kirchhoff's laws, part 1 of 2. Part 2 is Series, parallel and power.

Builds on Current, charge and potential difference.

IN THIS TOPIC

  • Recall the standard circuit symbols, and draw and interpret a circuit diagram built from them.
  • Apply conservation of charge at junctions and conservation of energy round loops.

COMMON MISCONCEPTION

Current gets used up on the way round.

Current is not used up: charge is conserved, so the current returning to the battery equals the current leaving it. What is transferred round the circuit is energy per coulomb, the pd.

The symbols, before the laws

Circuit diagrams use standard symbols, and every circuit in this unit is drawn with them. CIE prints a list of twenty-seven symbols in its syllabus and examines both directions: naming a symbol, and drawing and interpreting circuits built from them. OCR sets the same list, taken from the ASE booklet. AQA and Edexcel do not test the symbols on their own, but use them in their circuit questions, so the symbols are needed on every board.

The circuit symbols for sources, wiring and the components you put in the loop
Describe the drawing

A chart of fifteen circuit symbols, three to a row, each with its name printed underneath: cell, battery of cells, power supply, a.c. power supply, junction of conductors, switch, earth, fixed resistor, variable resistor, potentiometer, thermistor, light-dependent resistor, capacitor, diode and light-emitting diode.

FIG. 1The sources, the wiring and the components that go in the loop. A cell is one long thin plate and one short thick one, and the long thin plate is the positive terminal; a battery is two or more cells in a row, and a d.c. power supply is drawn the same way with its terminals marked. CIE prints a second form of the battery as well, a single long and short pair with a break drawn in the middle, standing for the same thing.

Three pairs of symbols are easily confused. A variable resistor has two terminals and an arrow across it, and it sets a current; a potentiometer has three, with the arrow coming in square to the element, and it sets a share of a pd. A thermistor takes a line across the element ending in a flat foot; an LDR takes two arrows pointing in at it, light arriving. A diode's triangle points the way conventional current is let through; an LED adds two arrows pointing away, light leaving.

The circuit symbols for the meters, and for the components a circuit drives
Describe the drawing

A chart of twelve circuit symbols, three to a row, each named underneath: ammeter, voltmeter, galvanometer, oscilloscope, lamp, heater, motor, generator, electric bell, buzzer, microphone and loudspeaker. The four meters are circles carrying the letters A, V, G and M, and the generator carries a G as well, so position in the circuit is what separates a generator from a galvanometer here. Boards do not all draw every one of these the same way, and the chart says so.

FIG. 2The meters, and the components a circuit drives. Each meter is a circle with a letter inside it; the oscilloscope gets a screen and a trace instead, and both of its leads come out of the same side because it is connected across a pair of points.

A meter is drawn as a circle with a letter inside it: A for an ammeter, V for a voltmeter, G for a galvanometer, and M for a motor, which is not a meter but uses the same outline. A generator also uses G, so the symbol alone does not distinguish it from a galvanometer; its position does. A generator is placed where a source would be, driving the circuit, while a galvanometer is placed in a branch, detecting currents too small for an ammeter.

Then the conventions for drawing one. Wires are straight lines meeting at right angles, and components sit on the straight runs rather than at the corners. A filled blob marks wires that are joined, and wires that cross without a blob are not connected. An ammeter goes in series with whatever it is counting, and is taken as having zero resistance; a voltmeter goes across whatever it is comparing, and is taken as having infinite resistance. Label every source with its emf and every component with its value.

One circuit diagram, read: the ammeter goes in the loop and the voltmeter goes across
Describe the drawing

A rectangular circuit diagram: a battery, a closed switch and an ammeter along the top wire, a lamp along the bottom, and a voltmeter on a branch that taps the bottom wire either side of the lamp at two junction blobs. The ammeter reads 0.30 amps and the voltmeter reads 6.0 volts across a 20 ohm lamp.

FIG. 3One circuit, read. The ammeter is part of the loop, so the 0.30 A it reads is the current in the lamp. The voltmeter hangs on a branch of its own between two blobs either side of the lamp, so the 6.0 V it reads is the pd across the lamp, and the ratio of the two readings is the lamp's 20 Ω.

WORKED EXAMPLE

Where the meters go

A lamp runs from a battery, and both the current through it and the pd across it are to be measured. Say where each meter goes, and what happens if the two are swapped.

An ammeter measures what passes, so it goes in series with the lamp, in the loop itself. Taken as having zero resistance, it changes nothing about the circuit it has joined.

A voltmeter compares two points, so it goes in parallel with the lamp, across it. Taken as having infinite resistance, it draws no current from the circuit it is connected across.

If they are swapped, the ammeter's zero resistance short-circuits the lamp and the voltmeter's infinite resistance breaks the loop. The lamp does not light and neither reading is valid, so the position of each meter is part of the measurement.

Kirchhoff's two laws

Circuit analysis rests on two statements known as Kirchhoff's laws, each of which is a conservation principle. The first is conservation of charge: charge does not accumulate at a junction, so the total current entering a junction equals the total current leaving it.

Then conservation of energy. Around any closed loop, the energy per unit charge supplied by the sources equals the energy per unit charge transferred in the components. Each series and parallel rule in the next lesson is one of these two laws applied to a particular arrangement.

Series circuits has moved to the next part of this lesson.

Parallel circuits has moved to the next part of this lesson.

More than one source in the loop has moved to the next part of this lesson.

Energy and power has moved to the next part of this lesson.

ASSESSMENT FOCUS

  • CIE and OCR examine the symbols in both directions: naming a symbol from the drawing, and drawing one from the name. Learn the list both ways.
  • A blob means the wires are joined; wires crossing without a blob are not connected. In a circuit you draw yourself, put the ammeter in the loop and the voltmeter across the component: both placements carry credit.
  • Current is not used up. An ammeter reads the same at every position in a series circuit; state this together with the conservation-of-charge reason.

CHECK YOURSELF

Three wires meet at a junction. One carries 0.80 A into it and another carries 0.35 A into it. State the current in the third wire and its direction, and name the law and the conservation principle you used. Then explain, to somebody who thinks current is used up, why an ammeter reads the same either side of a lamp.

Show a hint

The current into a junction equals the current out. For the lamp, consider which quantity is transferred, if not the charge.

Show the answer

The third wire carries 0.80 + 0.35 = 1.15 A out of the junction, because the current into a junction equals the current out of it.

That is Kirchhoff's first law, and it is a consequence of the conservation of charge: charge does not pile up at a point in the wire, so it leaves as fast as it arrives.

The same charge that enters a lamp leaves it, so the ammeter reads the same on both sides. What the lamp uses is energy, not charge: each coulomb arrives at a higher potential and leaves at a lower one, and the pd across the lamp is that drop.

Charge is conserved at every junction.

Energy is conserved round every loop.

WORKBOOK

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  • Recall the standard circuit symbols, and draw and interpret a circuit diagram built from them.
  • Apply conservation of charge at junctions and conservation of energy round loops.

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