Electrical power and energy consumption

A toaster connected to $230\ \text{V}$ has a current of $2\ \text{A}$ passing through it. Calculate its power in watts.

A mobile phone charger operates at $5\ \text{V}$ and delivers a current of $2\ \text{A}$. What power does it supply to the phone?

Order these appliances from lowest to highest typical power: an oven ($2500\ \text{W}$), an LED light bulb ($10\ \text{W}$), a television ($100\ \text{W}$) and a hairdryer ($1500\ \text{W}$), as shown in the figure.

Which converts more electrical energy per second?

An electric heater of $1150\ \text{W}$ is connected to the $230\ \text{V}$ mains. What current flows through it?

An oven rated at $2300\ \text{W}$ is connected to a $230\ \text{V}$ mains supply.

1. a) What current flows through it?
2. b) The kitchen socket and cable can withstand up to $16\ \text{A}$: is there a risk of overload using only the oven? Justify your answer.

On an electricity bill, consumption appears in $\text{kWh}$. Is the kilowatt-hour a unit of power or of energy? Explain in your own words what consuming $1\ \text{kWh}$ means.

A light bulb of $100\ \text{W}$ remains turned on for $10\ \text{h}$.

1. a) How much energy does it consume, in watt-hours?
2. b) Express it in kilowatt-hours.

A fan rated at $50\ \text{W}$ is turned on for $4\ \text{h}$. How much energy does it consume? Express it in $\text{Wh}$ and in $\text{kWh}$.

A camping battery stores $1\ \text{kWh}$ of energy.

1. a) How many hours can it power a portable fridge of $50\ \text{W}$?
2. b) And a light bulb of $10\ \text{W}$? Explain why it lasts longer with one than with the other.

Aoife says: "My hairdryer is very powerful: it uses $2000\ \text{kWh}$."

1. a) Correct the sentence: which unit corresponds to power?
2. b) Explain the difference between power and energy using the hairdryer example.
3. c) If the hairdryer is rated at $2000\ \text{W}$ and is used for $15\ \text{min}$, how much energy does it consume, in $\text{kWh}$?

A heater rated at $1200\ \text{W}$ is turned on for $2\ \text{h}$ a day during a month of $30$ days.

1. a) Express its power in kilowatts.
2. b) Calculate the energy it consumes in the month, in $\text{kWh}$.
3. c) If the price is $0.20\ \text{€/kWh}$, how much does this usage cost?

We leave the house for a whole day and accidentally leave a $100\ \text{W}$ lamp turned on for $10\ \text{h}$.

1. a) How many $\text{kWh}$ has it consumed?
2. b) How much money have we wasted, at $0.20\ \text{€/kWh}$?

The household electricity tariff has two prices: $0.30\ \text{€/kWh}$ during peak hours and $0.10\ \text{€/kWh}$ during off-peak hours. The washing machine, rated at $2\ \text{kW}$, runs a cycle lasting $2\ \text{h}$.

1. a) How much does it cost to run it during peak hours?
2. b) And during off-peak hours?
3. c) If $12$ wash loads are run per month, how much is saved per month by always running them off-peak?

On the energy rating label of a fridge, a letter between A and G appears.

1. a) What does this letter indicate?
2. b) Which letter should be chosen to pay less on the electricity bill? Why?

The label of a new fridge indicates a consumption of $150\ \text{kWh}$ per year, whereas the old one at home consumes $450\ \text{kWh}$ per year.

1. a) How many $\text{kWh}$ are saved each year with the new one?
2. b) How much money does this saving represent at $0.20\ \text{€/kWh}$?

An old television consumes $300\ \text{kWh}$ per year and a new LED television consumes $100\ \text{kWh}$ per year. The new television costs $\text{€}\ 400$ and $\text{kWh}$ is priced at $0.20\ \text{€/kWh}$.

1. a) How much money is saved each year with the new television?
2. b) How many years will it take for the savings to offset the cost of the television?
3. c) Do you think the replacement is worth it? Reason your answer using the data.

On this month's bill, $240\ \text{kWh}$ consumed at $0.20\ \text{€/kWh}$ appear.

1. a) How much does the energy consumed cost?
2. b) The family adjusts the thermostat on the electric water heater and manages to reduce consumption by $25\ \%$: how many $\text{kWh}$ do they save per month?
3. c) How much money does this saving amount to in a year?

A ceramic hob rated at $2\ \text{kW}$ operates for $15\ \text{min}$.

1. a) Express this time in hours.
2. b) Calculate the energy consumed, in $\text{kWh}$.
3. c) How much does it cost at $0.20\ \text{€/kWh}$?

A domestic installation allows a maximum of $3450\ \text{W}$ at any one time; if this is exceeded, the circuit breaker trips and the power goes out. The mains supply is $230\ \text{V}$. The diagram compares the power rating of the appliances with that maximum.

1. a) What maximum current does the installation allow?
2. b) Can we use the oven ($2300\ \text{W}$) and the washing machine ($2000\ \text{W}$) at the same time? Justify your answer with numbers.
3. c) What about the oven together with the microwave ($1150\ \text{W}$)?

Topic challenge. Become an energy auditor for your own home! Investigate your household electricity consumption to design a realistic energy-saving proposal:

1. Quantities and Ohm's law: Choose $3$ appliances connected to the mains ($V = 230\text{ V}$). Note the rated power ($P$) indicated on their labels and calculate the current ($I = P/V$) and resistance ($R = V/I$) of each one.

2. Experiment and data processing: Using your phone's stopwatch, measure the operating time of one of them (e.g., hairdryer or microwave) across $4$ different uses, considering an uncertainty of $t \pm 0.5\text{ s}$. Prepare a table with the times and energy consumed ($E = P \times t$, in $\text{kWh}$), and draw the $E$ versus $t$ graph by hand.

3. Circuit and real bill: Justify why the sockets in your home are connected in parallel and calculate the $R_{\text{eq}}$ if they were operating at the same time. Check today's average electricity pool price ($€/\text{kWh}$) on the Red Eléctrica de España (REE) website and calculate the weekly energy cost if they are used for $1.5\text{ h}$ per day (this is an estimate: the bill also includes network charges, levies and taxes).

Present your results in a brief report with a reasoned efficiency proposal.

Assessment criteria:

• Rigorous application of Ohm's law, powers, and parallel $R_{\text{eq}}$ calculation.

• Experimental data processing: table, graph, and inclusion of uncertainty ($\pm 0.5\text{ s}$).

• Correct use of real data from the REE and coherence of the proposed energy-saving measures.

An LED lamp rated at $10\ \text{W}$ provides the same light as an old bulb rated at $60\ \text{W}$, and both are turned on for $5\ \text{h}$ a day.

1. a) Calculate the energy consumed by each one in a month of $30$ days, in $\text{kWh}$.
2. b) With $\text{kWh}$ at $0.20\ \text{€/kWh}$, how much money is saved per month with the LED?

A games console has a power rating of $200\ \text{W}$ and you use it for $3\ \text{h}$ a day.

1. a) How much energy does it consume per day?
2. b) How many $\text{kWh}$ does it consume in a month of $30$ days?
3. c) Calculate the monthly cost at $0.20\ \text{€/kWh}$.

At Aoife's house, the following are used every day: an oven rated at $2\ \text{kW}$ for $1\ \text{h}$, ten LED bulbs rated at $10\ \text{W}$ turned on for $5\ \text{h}$ and a fridge rated at $200\ \text{W}$ operating for $24\ \text{h}$.

1. a) Calculate the $\text{kWh}$ consumed by each appliance per day.
2. b) How many $\text{kWh}$ are consumed in total in a month of $30$ days?
3. c) How much is the bill for the month at $0.20\ \text{€/kWh}$?

At Nico's house, standby appliances (the TV turned off with the red light on, plugged-in chargers, the console in standby...) consume $20\ \text{W}$ continuously, $24\ \text{h}$.

1. a) How much energy do they consume per day, in $\text{kWh}$?
2. b) How many $\text{kWh}$ do they consume in a year of $365$ days?
3. c) How much money would be saved per year by unplugging them, at $0.20\ \text{€/kWh}$?
4. d) Do you consider this a significant saving? Justify your opinion using the data.

Which consumes more in a month of $30$ days: an air conditioner rated at $1.5\ \text{kW}$ used for $2\ \text{h}$ a day or twenty LED bulbs rated at $10\ \text{W}$ turned on for $10\ \text{h}$ a day?

1. a) Calculate the monthly consumption of each option, in $\text{kWh}$.
2. b) Which consumes more?
3. c) Calculate the monthly cost of each option at $0.20\ \text{€/kWh}$.