Grade by Grade
D. Physics: Principles and Applications of Electricity · Electricity: Charges, Circuits and Energy

Resistance and the Factors That Affect It

D2.3 D2.4 A1.1About 65 minutes
Learning goals
  • I can define resistance and use its symbol (R) and SI unit (the ohm, Ω).
  • I can explain what resistance does to current and to electrical energy.
  • I can predict how length, cross-sectional area, material and temperature affect the resistance of a wire.
  • I can explain how resistors, variable resistors and short circuits behave.

Words to know

resistance (R)
How much a material or component opposes the flow of electric current. R = V ÷ I. Unit: the ohm (Ω).
ohm (Ω)
The SI unit of resistance. A component has 1 Ω of resistance if 1 V across it makes 1 A flow through it (1 Ω = 1 V/A).
cross-sectional area
The area of the circle you would see if you cut straight across a wire. Thicker wires have a larger cross-sectional area.
resistor
A component made to have a known resistance, used to control current.
variable resistor (rheostat)
A resistor whose resistance can be changed, as in a dimmer switch or volume control.
short circuit
An unintended path with very low resistance, which lets a dangerously large current flow.
nichrome
An alloy of nickel and chromium with a high resistance. It is used in toaster and hair-dryer heating elements.

Why does a toaster glow but its cord stays cool?

The same current flows through a toaster's cord and through its heating wires. Yet the thin wires inside glow orange-hot while the cord stays cool. The difference is resistance: the heating wires are made to resist the current much more than the copper in the cord.

What is resistance?

Resistance (symbol R) measures how much a component opposes the flow of current. As electrons move through a material, they collide with its atoms. These collisions slow the flow and transfer energy to the atoms, which vibrate faster: the material heats up.

Resistance is defined as the potential difference across a component divided by the current through it:

R = V ÷ I

Its SI unit is the ohm (symbol Ω, the Greek letter omega), named after the German scientist Georg Ohm. 1 Ω = 1 V/A. Large resistances are given in kilohms (1 kΩ = 1000 Ω) and megohms (1 MΩ = 1 000 000 Ω).

For a fixed potential difference: more resistance means less current.

Worked example

Example 1: Calculate a resistance

A potential difference of 12 V across a car's headlight makes a current of 4.0 A flow through it. What is its resistance?

  1. V = 12 V, I = 4.0 A. Find R.
  2. R = V ÷ I = 12 V ÷ 4.0 A

R = 3.0 Ω

Four factors that affect the resistance of a wire

  1. Length. A longer wire has more resistance: the electrons have farther to go and more collisions. Double the length → about double the resistance.
  2. Cross-sectional area (thickness). A thicker wire has less resistance: there are more paths side by side for the electrons. Double the area → about half the resistance.
  3. Material. Some materials resist more than others. Silver and copper have very low resistance. Nichrome has much higher resistance, which is why it is used in heating elements.
  4. Temperature. For metals, a hotter wire has more resistance, because its atoms vibrate more and get in the electrons' way more often.
Lengthshortlower Rlonghigher RThickness (area)thicklower Rthinhigher RMaterialcopperlower Rnichromehigher RTemperaturecoollower Rhothigher R
In each panel, only one factor changes. Longer, thinner, higher-resistance material (nichrome), and hotter wires all have higher resistance.
Worked example

Example 2: Predict the effect

Wire A is copper, 1 m long and 1 mm² in area, with a resistance of 0.02 Ω. Wire B is copper, 3 m long, same area, same temperature. Wire C is copper, 1 m long and 2 mm² in area. Estimate the resistance of B and C.

  1. B: only the length changes. It is 3 times as long, so its resistance is about 3 times as large: 3 × 0.02 Ω = 0.06 Ω.
  2. C: only the area changes. It has twice the area, so its resistance is about half: 0.02 Ω ÷ 2 = 0.01 Ω.

B ≈ 0.06 Ω and C ≈ 0.01 Ω. Change one factor at a time and you can predict the result.

Resistors and variable resistors

A resistor is made to have a particular resistance so that it controls the current in a circuit, for example to protect an LED from too much current.

A variable resistor (rheostat) lets you change the resistance, often by sliding a contact along a coil of wire to change the length the current passes through. Dimmer switches, volume knobs and the speed control on some toys work this way. In a circuit diagram it is a resistor symbol with an arrow through it.

+−variable resistor(rheostat)lamp
A dimmer circuit. Turning up the variable resistor increases the resistance in the loop, which decreases the current, so the lamp gets dimmer.

Short circuits: when resistance is too low

A short circuit happens when current finds a path with almost no resistance, for example when a bare wire touches across a lamp's terminals, or across the two terminals of a battery. Because R is tiny, the current becomes very large. The wires and the battery can get hot enough to melt insulation or start a fire. Fuses and circuit breakers protect against this by opening the circuit when the current gets too high.

+−bare wire:almost 0 Ωlamp off
A short circuit (do not build this). The bare wire connects the two sides of the lamp with almost zero resistance, so nearly all the current takes the wire, the lamp goes out, and the large current heats the battery and wires.

Watch out!

  • More resistance means less current (for the same voltage), not more.
  • Thicker wires have less resistance. That is why long extension cords for heaters must be heavy-duty (thick).
  • A short circuit is not just "a shorter wire". It is a path that skips the load and has almost no resistance.
Hands-on activity

Straw model and an online simulation (scientific research and modelling)

You need: 3 drinking straws (two the same, one wider such as a smoothie straw), tape, a glass of water, and a device with internet (optional).

Part 1: straw model. Sipping water through a straw is like pushing charge through a wire.

  1. Sip water through one ordinary straw. Then tape two ordinary straws end to end (a longer "wire") and sip again. Then try the wide straw.
  2. Record which was hardest and which was easiest.

What to look for: the long straw is harder (like a longer wire with more resistance). The wide straw is easier (like a thicker wire with less resistance).

Part 2: simulation. Open the free PhET simulation "Resistance in a Wire" (University of Colorado). Change one slider at a time (resistivity, which depends on the material; length; area) and record what happens to R. Write one sentence for each factor, such as: "When I doubled the length, the resistance doubled."

Safety (grown-up note): Use a clean straw for each person.

Just for fun

Resistance is not futile! Without it, a toaster would never toast, a hair dryer would never get warm, and an old-style light bulb would never glow.

Your turn

1

What is resistance, and what is its SI unit?

2

A lamp has 6.0 V across it and 0.50 A through it. Find its resistance.

3

Wire X is twice as long as wire Y, and they are otherwise identical. Which has more resistance, and about how much more?

4

Why does a heating element get hot?

5

Name the four factors that affect a wire's resistance.

6

What happens to the current in a dimmer circuit when the variable resistor's resistance is increased?

More practice: warm-up

1

Convert 4.7 kΩ to ohms.

2

Does a thicker wire have more or less resistance?

3

Which has lower resistance: copper or nichrome?

4

What is the symbol for resistance?

5

What is a short circuit?

More practice: on your own

1

A toaster element has a resistance of 16 Ω and a current of 7.5 A. What is the potential difference across it?

2

Why are the wires in a house thicker for an electric stove than for a lamp?

3

A copper wire has a resistance of 0.30 Ω. What would be the resistance of a copper wire at the same temperature that is half as long and has twice the area?

4

A filament lamp's resistance is higher when it is lit than when it is cold. Explain.

5

Explain why a short circuit across a battery is dangerous.

Challenge

1

A student wants to investigate how length affects the resistance of nichrome wire. Write a hypothesis, and name the independent, dependent and controlled variables.

2

Two wires are made of the same material. Wire P is 2 m long with an area of 1 mm². Wire Q is 4 m long with an area of 2 mm². Compare their resistances.

3

Superconductors are materials that have zero resistance when cooled to very low temperatures. Suggest one advantage of using them in power lines and one challenge.

Check your understanding

Quiz

1.

What is the SI unit of resistance?

2.

Which wire has the lowest resistance (same temperature)?

3.

A device has 9.0 V across it and 3.0 A through it. Its resistance is:

4.

If the resistance in a circuit increases while the voltage stays the same, the current:

5.

As a metal wire gets hotter, its resistance usually:

6.

Why is a short circuit dangerous?

For parents and teachers

Big idea: Resistance (R, in ohms) is one of the electrical quantities named in D2.3, and it is needed for the current–voltage–resistance investigation in the next lesson (D2.4). The PhET simulation supports research and modelling skills (A1.1).

Common difficulties:

  • Thicker wire = more resistance? No: thicker = less (more room for the current).
  • Rearranging R = V ÷ I. Practise: V = I × R, I = V ÷ R.
  • Short circuit meaning. It is a path that bypasses the load with nearly zero resistance.

How to help: Point out thick cords on heaters and stoves and thin cords on lamps and chargers, and ask why. Never let your teen connect a wire directly across a battery's terminals: it gets hot quickly.