Chapter 4 of 8

All 8 chapters
  1. 1Charge and current, readunderstood
  2. 2Potential difference, readunderstood
  3. 3Ohm's law, readunderstood
  4. 4Different components, readunderstood
  5. 5Series circuits, readunderstood
  6. 6Parallel circuits, readunderstood
  7. 7Power in circuits, readunderstood
  8. 8Mains electricity and safety, readunderstood

S4.12.4 Chapter 4

Different components

A resistor gives a straight line on a graph of current against p.d. Does a lamp do the same? What about a diode?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

  • You picked D. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Compare current and voltage graphs for a resistor, a lamp and a diode
  • Explain how thermistors and light dependent resistors work in sensors

A resistor at a steady temperature follows Ohm's law, and its graph is a straight line through the origin. Many useful parts do not. Their graphs curve or bend, and the shape of the graph tells you what the part does.

Start with a filament lamp. Its filament is a thin coil of metal wire. As the current grows, the filament gets hotter. Its atoms vibrate more, and the moving electrons bump into them more often. So the resistance rises as the filament gets hot. Ohm's law needs a steady temperature, and here the temperature changes.

Look at the graph of a lamp beside a graph of an 8 Ω resistor. We draw only the part for a battery joined the usual way. Reverse the battery and the current reverses. The curve repeats upside down and back to front: at −3 V the current is −0.5 A.

A graph with the axes current (A) and potential difference (V). The p.d. runs from 0 to 8 V in steps of 1 and the current from 0 to 1 A in steps of 0.25. A dashed straight line runs through the origin to 1 A at 8 V and is labelled resistor. A curve through the origin is labelled lamp. It is above the line up to 6 V, where it crosses the line at 0.75 A, and below the line after that. Two dots on the lamp curve, at 3 V and 0.5 A and at 6 V and 0.75 A, with dashed lines to both axes. Labels: current (A), potential difference (V), resistor, lamp.resistorlamp123456780.250.50.7510potential difference (V)current (A)
A resistor of 8 Ω and a filament lamp. The dashed lines mark the lamp at 3 V, with 0.5 A, and at 6 V, with 0.75 A. At 6 V the lamp has 8 Ω, the same as the resistor, so the two meet. The curve bends over, so each extra volt gives less extra current.

Find the resistance of the lamp at each point by dividing the p.d. by the current at that point. Do not use the gradient of the curve. R = V ÷ I works at any point, for any part.

See it three ways

As a picture

A table with the columns V (V), I (A) and V ÷ I (Ω). Row 1: 3, 0.5, 6. Row 2: 6, 0.75, 8.V (V)I (A)V ÷ I (Ω)30.5660.758

In words

At 3 V the lamp has a resistance of 6 Ω. At 6 V it has 8 Ω. The hotter filament has the larger resistance.

In symbols

R = V ÷ I. At 3 V: 3 ÷ 0.5 = 6 Ω. At 6 V: 6 ÷ 0.75 = 8 Ω.

A real lamp filament, white hot, can have a resistance ten times its cold value. This lamp rises by much less, so that the numbers stay small.

Next, the diode. A diode lets current through in one direction only. Its symbol is a triangle and a bar. Current can go the way the triangle points. Joined that way round, a silicon diode lets almost no current through until the p.d. across it is about 0.6 V. Above that, the current rises very steeply.

Joined the other way round, a diode lets almost no current through, however big the p.d. A p.d. far too big will damage it, but within its limits the current is close to zero.

A graph with the axes current (A) and p.d. (V). The p.d. runs from −0.4 to 1 V in steps of 0.2 and the current from −0.1 to 0.5 A in steps of 0.1. A curve lies along the p.d. axis at almost zero current for negative p.d.s and for p.d.s up to about 0.6 V, and then rises very steeply to the top of the graph near 0.9 V. A dot on the curve at 0.6 V has dashed lines to both axes, labelled 0.6 V. Labels: current (A), p.d. (V), diode, 0.6 V.0.6 Vdiode−0.40.40.8−0.10.10.20.30.40.50p.d. (V)current (A)
A diode. To the left of the current axis it is joined the other way round, and the current is almost zero. To the right, there is almost none until about 0.6 V, and then the current climbs steeply.

To see which way a diode lets current through, follow the conventional current round the loop. In a loop with a battery, the current leaves the + end. If it goes the way the triangle points, the lamp lights. If the diode is turned round, the loop is blocked.

Two loops, one above the other, each with a battery of two cells, marked + at the top and − at the bottom, with the label 3 V. In the top loop a diode labelled diode on the top wire points right, the way the current goes. The lamp on the right wire is lit and arrowheads on the wires point clockwise. In the bottom loop the diode is turned to point left. The lamp is dark. Labels: 3 V, diode, lamp, +, −, 3 V, diode, lamp, +, −.+−3 Vdiodelamp+−3 Vdiodelamp
Above, the diode points the way the current goes and the lamp lights. Below, it is turned round and the lamp is dark.

Try it

A diode in a torch

You need: a plain LED torch that takes two or three torch cells, such as AA cells.

Be safe: Use only ordinary torch cells. Leave the cells reversed for a few seconds only. Do not do this with rechargeable cells, or with cells that are damaged or hot. If the turned round cells do not touch the contacts, stop and do not force them. Skip this with a torch you cannot do without. Never open anything that plugs in to a socket.

  1. Switch on the torch. It lights. An LED is a diode that gives out light, so it works one way round only. This works best with a plain torch: cells, a switch and the LED.
  2. Switch off. Open the torch and take out the cells. Look at the + marks.
  3. Put all the cells back the wrong way round, so that every + end is where a − end was. Switch on and look.
  4. Switch off. Take the cells out and put them back the right way round.

What you will see: With the cells the right way round the LED lights. With every cell reversed the LED is joined the wrong way round, so no current goes through it and it stays dark. This is the diode working. A torch with a small circuit board inside may stay dark for another reason. Then the test does not show that the diode did it.

If you cannot try it, this is what happens.
A table with the columns Cells and Light. Row 1: right way, on. Row 2: reversed, off.CellsLightright wayonreversedoff

Now two parts whose resistance changes with the world around them. A thermistor is a resistor whose resistance depends on its temperature. The kind in this chapter is called NTC. As it gets hotter, its resistance falls. In this material, heating frees more charge carriers, so more can carry the current. A metal filament does the opposite.

A graph with the axes resistance (Ω) and temperature (°C). The temperature runs from 0 to 100 °C in steps of 20 and the resistance from 0 to 400 Ω in steps of 100. A curve starts at 400 Ω at 0 °C and falls, quickly at first and then more slowly, to 12.5 Ω at 100 °C. Two dots on the curve have dashed lines to both axes: 200 Ω at 20 °C and 50 Ω at 60 °C, labelled 200 Ω and 50 Ω. Labels: resistance (Ω), temperature (°C), thermistor, 200 Ω, 50 Ω.200 Ω50 Ωthermistor204060801001002003004000temperature (°C)resistance (Ω)
An NTC thermistor. This one halves its resistance for every 20 °C. Other thermistors have other numbers, but the same shape.

Put a thermistor in a loop with a battery and an ammeter. At 20 °C its resistance is 200 Ω. The current is 6 V ÷ 200 Ω = 0.03 A. At 60 °C its resistance is 50 Ω, so the current is 6 V ÷ 50 Ω = 0.12 A. The ammeter reading follows the temperature.

A table with the columns T (°C), R (Ω) and I (A). Row 1: 20, 200, 0.03. Row 2: 60, 50, 0.12.T (°C)R (Ω)I (A)202000.0360500.12
The same thermistor in a loop with a 6 V battery and an ammeter. Hotter means less resistance and more current.

The current shows the temperature. A fire alarm or a thermostat can use this. Electronic parts watch the current or a p.d. When it passes a set value, they switch on a buzzer or a heater. The thermistor does the sensing. The electronics do the switching.

A light dependent resistor, or LDR, works the same way with light. When bright light falls on it, its resistance falls. In the dark, its resistance is very high, often about a million ohms (1 MΩ) or more. Light is measured in lux. A bright room has some hundreds of lux.

A graph with the axes resistance (kΩ) and light level (lux). The light level runs from 0 to 180 lux in steps of 30 and the resistance from 0 to 1 000 kΩ in steps of 200. A curve starts at 1 000 kΩ in the dark and falls steeply and then more slowly to 100 kΩ at 180 lux. Two dots on the curve have dashed lines to both axes: 400 kΩ at 30 lux and 100 kΩ at 180 lux, labelled 400 kΩ and 100 kΩ. Labels: resistance (kΩ), light level (lux), LDR, 400 kΩ, 100 kΩ.400 kΩ100 kΩLDR3060901201501802004006008001 0000light level (lux)resistance (kΩ)
An example LDR. More light, less resistance.

One kilohm, kΩ, is 1 000 Ω. A p.d. in volts divided by a resistance in kilohms gives a current in milliamps, mA. For example 6 V ÷ 100 kΩ = 0.06 mA. Use this, or change to ohms and amps first.

A table with the columns E (lux), R (kΩ) and I (mA). Row 1: 0, 1 000, 0.006. Row 2: 180, 100, 0.06.E (lux)R (kΩ)I (mA)01 0000.0061801000.06
The same LDR in a loop with a 6 V battery and an ammeter. Brighter light means less resistance and more current.
A list of four circuit symbols, each on a short wire with its name beside it: diode, a triangle and a bar, thermistor, a rectangle with a sloping line and a hook, LDR, a rectangle with two arrows pointing at it, and lamp, a circle with a cross. Labels: diode, thermistor, LDR, lamp.diodethermistorLDRlamp
The four symbols of this chapter. The two arrows on the LDR are the light falling on it.

Worked example

A thermistor has a resistance of 200 Ω. It is joined to a 6 V battery. What current flows?

  1. Write the equation for the current: I = V ÷ R.
  2. Put in the numbers: I = 6 V ÷ 200 Ω = 0.03 A.
  3. The current is 0.03 A.

Answer: 0.03 A

Worked example

An LDR has a resistance of 30 kΩ in bright light. It is joined to a 6 V battery. What current flows, in milliamps?

  1. Change to ohms: 30 kΩ = 30 × 1 000 = 30 000 Ω.
  2. Write the equation for the current: I = V ÷ R.
  3. Put in the numbers: I = 6 V ÷ 30 000 Ω = 0.0002 A.
  4. Change to milliamps: 0.0002 A × 1 000 = 0.2 mA.

Answer: 0.2 mA

A wrong idea many people have

Every part that has a resistance follows Ohm's law, so every I-V graph is a straight line.

Why it feels right: We write V = IR for everything, and a resistor gives a straight line, so it seems that all parts should.

The test that breaks it: Look at the lamp curve. At 3 V the lamp had 6 Ω and at 6 V it had 8 Ω. V ÷ I changes, so the graph cannot be a straight line through the origin.

What is true: V = IR gives the resistance of any part at any moment. Ohm's law is the extra fact that R stays the same. A resistor at a steady temperature follows it. A lamp, a diode and a thermistor do not.

A wrong idea many people have

A thermistor gets a bigger resistance when it gets hotter, like the filament of a lamp.

Why it feels right: We know that hot metal has more resistance, and a thermistor is also a kind of resistor.

The test that breaks it: Look at the thermistor graph. At 20 °C it has 200 Ω and at 60 °C only 50 Ω. The curve falls as the temperature rises.

What is true: In an NTC thermistor, heating frees more charge carriers, so the resistance falls. In a metal, heating makes the atoms vibrate more, so the resistance rises. The two parts behave differently.

A wrong idea many people have

The resistance of the lamp at a point is the gradient of its curve at that point.

Why it feels right: On many graphs the gradient is the quantity of interest.

The test that breaks it: Take the point 6 V and 0.75 A. V ÷ I gives 8 Ω. The slope of the curve there is about 0.06 A for each volt, and 1 ÷ 0.0625 is 16 Ω, a different number.

What is true: The resistance at a point is the p.d. there divided by the current there. This is true whatever the shape of the curve.

Key words

filament lamp
a lamp with a thin coil of wire that glows when hot. Its resistance rises as it heats.
diode
a part that lets current through one way only, above about 0.6 V for a silicon diode.
thermistor
a resistor whose resistance changes with temperature. An NTC thermistor falls in resistance as it gets hotter.
light dependent resistor
a resistor whose resistance falls as the light on it gets brighter. It is called an LDR for short.
kilohm
one thousand ohms, written kΩ.

Back to your guess

The answer is C: No, a lamp and a diode both give curves, and a diode lets current through one way only.

Only an ohmic conductor at a steady temperature gives a straight line through the origin. A filament lamp gives a curve, because its resistance rises as it heats. A diode lets current through one way and almost none the other way.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Will the lamp in the loop light?

    A loop with a battery of two cells on the left, marked + at the top and − at the bottom, with the label 3 V. A closed switch labelled switch is on the top wire. A diode labelled diode on the bottom wire has its triangle pointing right. The lamp labelled lamp on the right wire is dark. Labels: 3 V, switch, diode, lamp, +, −.+−3 Vswitchdiodelamp
    Tap your answer.

    1. Yes, that is right. Conventional current leaves the + end, goes along the top, down the right and back to the left along the bottom. The diode on the bottom points right, against that current, so it blocks it and the lamp stays dark.

    2. Not this one. A diode lets current through one way only. In the other direction it lets almost none through. Try another.

    3. Not this one. On the bottom wire the current goes to the left, not the right. Follow it from the + end, along the top and down the right side. Try another.

    4. Not this one. A closed switch lets current through. It is the diode that blocks the loop. Try another.

    See the answer

    No, because the diode is the wrong way round for the current

    Conventional current leaves the + end, goes along the top, down the right and back to the left along the bottom. The diode on the bottom points right, against that current, so it blocks it and the lamp stays dark.

    • If you chose B: A diode lets current through one way only. In the other direction it lets almost none through.
    • If you chose C: On the bottom wire the current goes to the left, not the right. Follow it from the + end, along the top and down the right side.
    • If you chose D: A closed switch lets current through. It is the diode that blocks the loop.

  2. The graph shows the resistance of a thermistor at different temperatures. What is its resistance at 40 °C?

    A graph with the axes resistance (Ω) and temperature (°C). The temperature runs from 0 to 100 °C in steps of 20 and the resistance from 0 to 400 Ω in steps of 100. A curve starts at 400 Ω at 0 °C and falls, quickly at first and then more slowly, to 12.5 Ω at 100 °C. Labels: resistance (Ω), temperature (°C).204060801001002003004000temperature (°C)resistance (Ω)
    Tap your answer.

    1. Not this one. You took the middle of 200 Ω and 50 Ω. The curve is not a straight line between them, so read the curve itself at 40 °C. Try another.

    2. Not this one. That is the resistance at 20 °C. Go along to 40 °C on the temperature axis, then up to the curve. Try another.

    3. Yes, that is right. Go up from 40 °C to the curve and across to the resistance axis: 100 Ω. It has halved twice from 400 Ω, once for each 20 °C.

    4. Not this one. You read the temperature as the resistance. Go up from 40 °C to the curve, then across to the resistance axis. Try another.

    See the answer

    100 Ω

    Go up from 40 °C to the curve and across to the resistance axis: 100 Ω. It has halved twice from 400 Ω, once for each 20 °C.

    • If you chose A: You took the middle of 200 Ω and 50 Ω. The curve is not a straight line between them, so read the curve itself at 40 °C.
    • If you chose B: That is the resistance at 20 °C. Go along to 40 °C on the temperature axis, then up to the curve.
    • If you chose D: You read the temperature as the resistance. Go up from 40 °C to the curve, then across to the resistance axis.

  3. The graph is for a filament lamp. What is the resistance of the lamp when the p.d. across it is 4 V?

    A graph with the axes current (A) and potential difference (V). The p.d. runs from 0 to 6 V in steps of 1 and the current from 0 to 1.2 A in steps of 0.1. A curve starts at the origin, climbs steeply at first and bends over, reaching 1 A at 6 V. Labels: current (A), potential difference (V).1234560.20.40.60.811.20potential difference (V)current (A)
    Tap your answer.

    1. Not this one. That is the current at 4 V, read as a resistance. Divide the p.d. by the current. Try another.

    2. Not this one. You multiplied 4 V by 0.8 A. The resistance is the p.d. divided by the current. Try another.

    3. Not this one. You divided the current by the p.d., the wrong way round. R = V ÷ I. Try another.

    4. Yes, that is right. At 4 V the curve is at 0.8 A. R = V ÷ I = 4 V ÷ 0.8 A = 5 Ω.

    See the answer

    5 Ω

    At 4 V the curve is at 0.8 A. R = V ÷ I = 4 V ÷ 0.8 A = 5 Ω.

    • If you chose A: That is the current at 4 V, read as a resistance. Divide the p.d. by the current.
    • If you chose B: You multiplied 4 V by 0.8 A. The resistance is the p.d. divided by the current.
    • If you chose C: You divided the current by the p.d., the wrong way round. R = V ÷ I.

  4. A street light uses an LDR to switch on at dusk. As the evening gets darker, what happens to the resistance of the LDR?

    Tap your answer.

    1. Not this one. It is the other way round. The LDR has less resistance in bright light and more in the dark. Try another.

    2. Yes, that is right. An LDR has a high resistance in the dark and a low one in bright light. As the evening darkens its resistance rises, so the current in its loop falls, and the electronics can switch the lamp on.

    3. Not this one. If the resistance did not change, the LDR could not sense the light. Its resistance changes with the light level. Try another.

    4. Not this one. In the dark the resistance is very high, not zero. A resistance of zero would be a plain wire. Try another.

    See the answer

    It rises

    An LDR has a high resistance in the dark and a low one in bright light. As the evening darkens its resistance rises, so the current in its loop falls, and the electronics can switch the lamp on.

    • If you chose A: It is the other way round. The LDR has less resistance in bright light and more in the dark.
    • If you chose C: If the resistance did not change, the LDR could not sense the light. Its resistance changes with the light level.
    • If you chose D: In the dark the resistance is very high, not zero. A resistance of zero would be a plain wire.

  5. Why is the graph of current against p.d. for a filament lamp a curve?

    Tap your answer.

    1. Not this one. The filament is a metal wire and a good conductor. The curve comes from its changing temperature. Try another.

    2. Not this one. It is the other way round. The graph flattens, so each extra volt gives less extra current: the resistance rises. Try another.

    3. Yes, that is right. A bigger current heats the filament more. The hotter metal has a bigger resistance, so each extra volt adds less current and the curve flattens.

    4. Not this one. The graph is drawn for each p.d. we set. The curve comes from the lamp itself, not the battery. Try another.

    See the answer

    Its resistance rises as the filament gets hotter

    A bigger current heats the filament more. The hotter metal has a bigger resistance, so each extra volt adds less current and the curve flattens.

    • If you chose A: The filament is a metal wire and a good conductor. The curve comes from its changing temperature.
    • If you chose B: It is the other way round. The graph flattens, so each extra volt gives less extra current: the resistance rises.
    • If you chose D: The graph is drawn for each p.d. we set. The curve comes from the lamp itself, not the battery.

  6. A thermistor in a fire alarm gets hotter. What happens to its resistance and to the current through it?

    Tap your answer.

    1. Not this one. That is how a metal wire behaves. An NTC thermistor behaves the other way. Try another.

    2. Yes, that is right. An NTC thermistor loses resistance as it heats. With the same p.d., I = V ÷ R, so the current rises, and the electronics can switch on the alarm.

    3. Not this one. With less resistance and the same p.d., the current rises. Use I = V ÷ R. Try another.

    4. Not this one. The resistance of a thermistor depends on its temperature. That is why we use it. Try another.

    See the answer

    The resistance falls and the current rises

    An NTC thermistor loses resistance as it heats. With the same p.d., I = V ÷ R, so the current rises, and the electronics can switch on the alarm.

    • If you chose A: That is how a metal wire behaves. An NTC thermistor behaves the other way.
    • If you chose C: With less resistance and the same p.d., the current rises. Use I = V ÷ R.
    • If you chose D: The resistance of a thermistor depends on its temperature. That is why we use it.

  7. Which of these follows Ohm's law?

    Tap your answer.

    1. Not this one. The resistance of a lamp rises as it heats, so its graph is a curve. Try another.

    2. Not this one. A diode lets current through one way and almost none the other. Its graph is not a straight line through the origin. Try another.

    3. Not this one. The resistance of a thermistor changes with its temperature, so V ÷ I is not constant. Try another.

    4. Yes, that is right. Only a part whose resistance stays the same follows Ohm's law. A resistor at a steady temperature does. The other three have resistances that change.

    See the answer

    A resistor at a steady temperature

    Only a part whose resistance stays the same follows Ohm's law. A resistor at a steady temperature does. The other three have resistances that change.

    • If you chose A: The resistance of a lamp rises as it heats, so its graph is a curve.
    • If you chose B: A diode lets current through one way and almost none the other. Its graph is not a straight line through the origin.
    • If you chose C: The resistance of a thermistor changes with its temperature, so V ÷ I is not constant.

  8. From an earlier chapter

    A resistor of 15 Ω carries a current of 0.6 A. What is the p.d. across it?

    Tap your answer.

    1. Yes, that is right. V = IR = 0.6 A × 15 Ω = 9 V.

    2. Not this one. You divided the resistance by the current. The p.d. is the product: V = IR. Go to S4.12.3. Try another.

    3. Not this one. You divided the current by the resistance. Multiply instead. Go to S4.12.3. Try another.

    4. Not this one. You added the two numbers. V = IR is a product. Go to S4.12.3. Try another.

    See the answer

    9 V

    V = IR = 0.6 A × 15 Ω = 9 V.

    • If you chose B: You divided the resistance by the current. The p.d. is the product: V = IR. Go to S4.12.3.
    • If you chose C: You divided the current by the resistance. Multiply instead. Go to S4.12.3.
    • If you chose D: You added the two numbers. V = IR is a product. Go to S4.12.3.

  9. A filament lamp has 9 V across it and a current of 1.2 A through it. Find its resistance at that moment.

    See the answer

    7.5 Ω

    R = V ÷ I = 9 V ÷ 1.2 A = 7.5 Ω.

  10. An LDR with a resistance of 36 kΩ is joined to a 9 V battery. What current flows, in milliamps?

    See the answer

    0.25 mA

    R = 36 kΩ, and V ÷ R in kΩ gives mA. I = 9 V ÷ 36 kΩ = 0.25 mA.

Keep it

Copy this into your exercise book.

Resistor: straight I-V line. Lamp: curve, resistance rises as it heats. Diode: one way only, above 0.6 V. Thermistor: R falls as hotter. LDR: R falls as brighter.

Draw: Axes of current and p.d. Sketch a straight line for a resistor, a bending curve for a lamp and a flat then steep curve for a diode.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (977 KB). It opens on any phone.