Concepts addressed: **velocity in an electric field, electrical power, and analytical skills.**

Grade level: 11th

**Scenario:**

When a light **switch is off**, the electric circuit inside the wall of your house is interrupted, so **neither an electric field nor electrons can flow through it**. The moment you flip the **switch on** you close the circuit, meaning that electrons (and the electric field) are **free to flow through the circuit again**, and reach whatever device you wanted to power.

Assuming the wiring in your house is full copper 12AWG, and that the length of the cable connecting the switch to the overhead light bulb (60W LED) is 3m.

- How long would it take an electron in the switch to reach the light bulb?
- Is the result surprising? Why?
- Can you explain it? How long would it take light to travel the same distance?

**Data:**

Diameter of 12 AWG wire: 2.053mm

Voltage of household’s electric system: 220V (EU) || 120V (US)

Density of Carriers in copper: 8.5 1028 carriers/m³

Speed of light: 299 792 458 m/s

**Useful calculators:**

- Circumference calculator – https://www.omnicalculator.com/math/circumference
- Wire Resistance calculator – https://www.omnicalculator.com/physics/wire-resistance
- Ohm’s Law calculator – https://www.omnicalculator.com/physics/ohms-law
- Drift Velocity calculator – https://www.omnicalculator.com/physics/drift-velocity
- Velocity calculator – https://www.omnicalculator.com/physics/velocity

**Question 1 hints:**

Solve for time.

**Question 2 hints:**

**Question 3 hints:**

**Solutions :**

**75.1 hours**to travel 3m of cable.

**Yes**.

Because the light turns on immediately

**it takes light 0.00000001000692 seconds**to travel 3m

**Step-by-Step solutions :**

**u = I / (n * A * e)**where

*u*is the drift velocity,

*e*is the electron charge, I is the electrical current,

*A*is the cross section area of the cable and

*n*is the density of free electrons in the cable (copper).

The value of n is given, and A can be calculated using A = π r

^{2}, or by using the Circumference calculator. We find that A = 13.24mm

^{2}.

To calculate I, we can use the power draw formula: P = IV. For a standard American household, V = 120V, and our bulb is 60W, so we get I = 0.5A.

Plugging this data into the Drift Velocity calculator gives a

**speed of 0.000002773m/s.**

All we need to do is use that speed and the length of the cable (distance travelled) to calculate time using V = d/t. You can do it by hand or with a calculator, and you will see that

**it takes the electrons 75.1 hours**to travel along 3m of cable.

**Yes it is surprising**.

Because it takes hours for an electron to travel the length of the cable, yet the light turns on almost instantly.

**electrons so close to the light bulb that it takes them almost no time to reach it**once the electric field gets there.

A bonus:what are you teaching next week? We'd love to prepare a scenario for you 🙂