P7: Electrical Power and Energy
Power, energy transfers and the National Grid โ including electrical power equations, transformers, mains electricity and safety.
๐ Key Definitions
Power: The rate at which energy is transferred. Measured in watts (W). 1 watt = 1 joule per second.
The National Grid: A network of cables and transformers that connects power stations to consumers (homes and industry) across the UK.
Transformer: A device that changes the voltage of an alternating current (AC). Step-up transformers increase voltage; step-down transformers decrease voltage.
๐ Power Equations
P = E / t (power = energy transferred / time)
P = V x I (power = potential difference x current)
P = I x I x R (power = current squared x resistance)
P = V x V / R (power = voltage squared / resistance)
Where:
- P = power, in watts (W)
- E = energy, in joules (J)
- t = time, in seconds (s)
- V = potential difference, in volts (V)
- I = current, in amperes (A)
- R = resistance, in ohms (ฮฉ)
๐ Energy Transferred Equations
E = P x t (energy = power x time)
E = Q x V (energy = charge flow x potential difference)
Where:
- Q = charge flow, in coulombs (C)
- V = potential difference, in volts (V)
โก The National Grid
The National Grid distributes electricity from power stations to consumers. To reduce energy loss in the cables, electricity is transmitted at very high voltage and low current.
Step-up Transformers
- Located at power stations
- Increase the voltage (to 400 000 V or 275 000 V)
- Decrease the current proportionally
- Why? Lower current means less energy dissipated as heat in the cables (P = I x I x R), so less energy is wasted
Step-down Transformers
- Located near homes and industry (at substations)
- Decrease the voltage to a safe level (230 V for homes)
- Increase the current proportionally
- Why? 230 V is safe for domestic use; high voltage would be dangerous
| Transformer | Voltage | Current | Location |
|---|---|---|---|
| Step-up | Increases | Decreases | Power station |
| Step-down | Decreases | Increases | Substation (near homes) |
๐ Mains Electricity
UK mains supply: 230 V AC (alternating current) at 50 Hz. AC means the current changes direction 50 times per second.
Three-Core Cable
| Wire | Colour | Function | Danger |
|---|---|---|---|
| Live | Brown | Carries alternating current from the supply (230 V) | Most dangerous โ gives a shock if touched |
| Neutral | Blue | Completes the circuit (0 V) | Normally safe, but can be dangerous if faulty |
| Earth | Green/yellow | Safety wire โ connects metal casing to ground | Carries current safely to ground if a fault occurs |
๐ก๏ธ Electrical Safety
Fuses: A thin wire that melts and breaks the circuit if the current gets too high. The fuse rating should be slightly above the normal operating current. Fuses are always placed in the live wire.
Circuit breakers: Electromagnetic switches that trip (open) when the current exceeds a safe value. They can be reset, unlike fuses which must be replaced.
Earthing: If a fault causes the live wire to touch the metal case of an appliance, the earth wire provides a low-resistance path to ground. A large current flows to earth, which blows the fuse and disconnects the appliance, protecting the user from a shock.
| Safety Device | How it works | Advantage | Disadvantage |
|---|---|---|---|
| Fuse | Wire melts when current is too high | Cheap, simple, reliable | Must be replaced after blowing, slower to react |
| Circuit breaker | Switch trips when current is too high | Can be reset, faster reaction | More expensive than fuses |
| Earth wire | Provides path to ground if fault occurs | Protects against electric shock from metal cases | Only works with metal-cased appliances |
๐ Worked Examples
Worked Example 1 โ Calculating Power from V and I
Question: A kettle is connected to a 230 V supply and draws a current of 10 A. Calculate the power of the kettle.
Solution:
P = V x I = 230 x 10 = 2300 W = 2.3 kW
Worked Example 2 โ Calculating Energy Transferred
Question: A 2 kW heater is left on for 3 hours. Calculate the energy transferred in joules and in kWh.
Solution:
Time = 3 x 3600 = 10 800 s
E = P x t = 2000 x 10 800 = 21 600 000 J = 21.6 MJ
In kWh: E = P (kW) x t (h) = 2 x 3 = 6 kWh
Worked Example 3 โ Calculating Power from I and R
Question: A current of 5 A flows through a resistor of 8 ฮฉ. Calculate the power dissipated.
Solution:
P = I x I x R = 5 x 5 x 8 = 200 W
Worked Example 4 โ Energy from Charge and Voltage
Question: A charge of 150 C flows through a component with a potential difference of 12 V across it. Calculate the energy transferred.
Solution:
E = Q x V = 150 x 12 = 1800 J
Worked Example 5 โ National Grid and Transformers
Question: A power station generates electricity at 25 000 V and 400 A. A step-up transformer increases the voltage to 400 000 V for transmission. Calculate the current in the transmission cables and explain why the voltage is stepped up.
Solution:
Power from power station: P = V x I = 25 000 x 400 = 10 000 000 W = 10 MW
At 400 000 V: I = P / V = 10 000 000 / 400 000 = 25 A
The voltage is stepped up so the current is reduced from 400 A to 25 A. Since energy loss in cables = I x I x R, reducing the current from 400 A to 25 A massively reduces the energy lost as heat in the transmission cables.
Worked Example 6 โ Choosing a Fuse
Question: An electric iron has a power rating of 920 W and is used on a 230 V supply. Calculate the normal operating current and choose an appropriate fuse (3 A, 5 A or 13 A).
Solution:
I = P / V = 920 / 230 = 4 A
The normal current is 4 A. The fuse should be rated slightly above this, so a 5 A fuse is appropriate. A 3 A fuse would blow during normal use; a 13 A fuse would not provide adequate protection.
โ Practice Questions
Q1: Foundation A hair dryer has a power of 1200 W and is connected to a 230 V supply. Calculate the current it draws.
Q2: Foundation Explain why the National Grid uses step-up transformers at power stations.
Q3: Foundation State the colour and function of each wire in a three-core mains cable.
Q4: Higher A 1500 W electric heater is used for 30 minutes. Calculate the energy transferred in (a) joules and (b) kWh.
Q5: Higher A 10 ฮฉ resistor has a current of 4 A flowing through it. Calculate the power dissipated using two different power equations and verify they give the same answer.
โ Answers
- I = P / V = 1200 / 230 = 5.22 A.
- Step-up transformers increase the voltage and decrease the current. Lower current means less energy is wasted as heat in the transmission cables (since power loss = I squared x R). This makes the National Grid more efficient.
- Live wire = brown, carries the 230 V current from the supply. Neutral wire = blue, completes the circuit at 0 V. Earth wire = green/yellow, safety wire that connects the metal case to the ground to protect against electric shock.
- (a) Time = 30 x 60 = 1800 s. E = P x t = 1500 x 1800 = 2 700 000 J = 2.7 MJ. (b) E = 1.5 kW x 0.5 h = 0.75 kWh.
- Using P = I x I x R = 4 x 4 x 10 = 160 W. Using P = V x I: first find V = I x R = 4 x 10 = 40 V. Then P = 40 x 4 = 160 W. Both give 160 W, confirming the equations are consistent.
๐ฏ Exam Tips
- Know all four power equations โ P = E/t, P = VI, P = IIR, P = VV/R โ and when to use each one.
- For energy calculations, always convert time to seconds if using joules, or use hours for kWh.
- When asked about the National Grid, always mention: high voltage reduces current, which reduces energy loss as heat (P = IIR).
- Know the wire colours: brown = live, blue = neutral, green/yellow = earth.
- Fuse choice: the fuse rating should be slightly above the normal operating current.
- When explaining earthing: live wire touches metal case โ large current flows to earth โ fuse blows โ circuit is disconnected โ user is safe.
- AC (alternating current) is used in mains; batteries supply DC (direct current). Know the difference.
๐ข Maths Skills
Mathematical Skills
You need to use four power equations fluently: P = E/t, P = VI, P = IยฒR, P = Vยฒ/R. For energy: E = Pt (joules when P in watts, t in seconds) and E = Pt (kWh when P in kW, t in hours). For fuse ratings: calculate the normal operating current using I = P/V, then choose the next standard fuse rating above it (3 A, 5 A or 13 A). Always convert units โ kW to W (ร1000), hours to seconds (ร3600), mA to A (รท1000).
Maths Example
An electric oven has a power rating of 7.2 kW and is connected to a 230 V supply. Calculate the current and choose an appropriate fuse.
I = P / V = 7200 / 230 = 31.3 A
Appropriate fuse: 13 A fuse is too low โ this appliance requires a dedicated high-current circuit with a 32 A circuit breaker, not a standard plug fuse.
โ ๏ธ Common Misconceptions
Watch Out!
1. Wrong: Power and energy are the same thing Correct: Power is the rate of energy transfer (watts); energy is the total transferred (joules or kWh). P = E/t โ they are related but not the same
2. Wrong: A higher power appliance always uses more energy Correct: Energy depends on power AND time. A 3 kW heater on for 10 minutes uses less energy than a 1 kW heater on for 1 hour
3. Wrong: Fuses "use" electricity Correct: Fuses do not consume energy โ they are safety devices that melt and break the circuit if the current exceeds their rating
โ๏ธ 6-Mark Question
Extended Answer
6 marks: Explain how the National Grid transmits electricity efficiently using step-up and step-down transformers. Refer to power, current, voltage and energy loss.
Electricity is generated at power stations at around 25 000 V. A step-up transformer at the power station increases the voltage to 400 000 V for transmission through the National Grid cables. Since power = voltage ร current, increasing the voltage means the current is reduced proportionally for the same power transmitted. Lower current is crucial because the energy lost as heat in the transmission cables depends on P = IยฒR โ even a small reduction in current causes a large reduction in power loss because the current is squared. This means less energy is wasted and more reaches the consumer. Near homes and industry, step-down transformers at substations reduce the voltage to 230 V for safe domestic use, which increases the current back to the level needed by appliances. Using transformers makes the grid efficient by minimising energy loss during long-distance transmission while delivering safe voltages to consumers.
Mark scheme: 1 mark โ step-up transformer increases voltage at power station, 1 mark โ current is reduced, 1 mark โ P = IยฒR explains energy loss in cables, 1 mark โ lower current means much less energy wasted as heat, 1 mark โ step-down transformer reduces voltage to 230 V near consumers, 1 mark โ reference to same power being transmitted or efficiency
๐ AO3: Analyse & Evaluate
Analysis and Evaluation
The table shows the power ratings and typical daily use of three household appliances on a 230 V supply. Electricity costs 28p per kWh.
| Appliance | Power | Daily use |
|---|---|---|
| Kettle | 2.2 kW | 12 minutes |
| Fridge | 150 W | 24 hours |
| Tumble dryer | 2.5 kW | 45 minutes |
(a) Calculate the daily energy consumption in kWh for each appliance. Which uses the most energy per day?
(b) Calculate the daily cost of running the fridge and the weekly cost (7 days). Why might the fridge's actual consumption be lower than calculated?
(c) A student claims "the tumble dryer costs the most to run because it has the highest power." Evaluate this claim using your calculations.
Answers: (a) Kettle: 2.2 ร (12/60) = 0.44 kWh. Fridge: 0.150 ร 24 = 3.6 kWh. Tumble dryer: 2.5 ร (45/60) = 1.875 kWh. The fridge uses the most energy per day. (b) Daily cost = 3.6 ร 28 = 100.8p โ ยฃ1.01. Weekly = ยฃ1.01 ร 7 = ยฃ7.07. The fridge has a thermostat so it does not run continuously โ it switches on and off to maintain temperature, so actual consumption is lower. (c) The claim is wrong. Despite having the highest power, the tumble dryer uses only 1.875 kWh/day because it runs for a short time. The fridge, with much lower power, uses 3.6 kWh/day because it runs for much longer. Energy depends on power AND time, not power alone.
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