CIE iGCSE Co-ordinated Sciences-P4.2.5 Electrical energy and electrical power- Study Notes- New Syllabus
CIE iGCSE Co-ordinated Sciences-P4.2.5 Electrical energy and electrical power – Study Notes
CIE iGCSE Co-ordinated Sciences-P4.2.5 Electrical energy and electrical power – Study Notes -CIE iGCSE Co-ordinated Sciences – per latest Syllabus.
Key Concepts:
Core
- Understand that electric circuits transfer energy from a source of electrical energy, such as an electrical cell or mains supply, to the circuit components and then into the surroundings
- Recall and use the equation for electrical power P = IV
- Recall and use the equation for electrical energy E = IVt
- Define the kilowatt-hour (kW h) and calculate the cost of using electrical appliances where the energy unit is the kWh
CIE iGCSE Co-Ordinated Sciences-Concise Summary Notes- All Topics
Energy Transfer in Electric Circuits
Electric circuits transfer energy from a source (battery, cell, or mains supply) to components in the circuit, and eventually into the surroundings.
Source of Electrical Energy:
An electrical cell, battery, or mains supply provides the electromotive force (e.m.f.) to push charges around the circuit.
- The source supplies energy per coulomb of charge to the circuit.
- Example: A 9 V battery supplies 9 J of energy to each coulomb of charge.
Transfer to Circuit Components:
As charges flow through circuit components, they transfer energy to them.
Examples:
- Lamp → electrical energy → light + heat.
- Motor → electrical energy → kinetic energy (motion) + heat.
- Heater → electrical energy → thermal energy.
Transfer to Surroundings:
- Some of the energy transferred to components is useful (light, motion, heating).
- The rest is often transferred to the surroundings as waste heat.
- Example: A filament bulb gives light but most energy is wasted as heat in the surroundings.
Conservation of Energy in Circuits:
- Total energy supplied by the source = total energy transferred to all circuit components and surroundings.
- This is consistent with the law of conservation of energy.
Example :
A 12 V car battery transfers energy to a headlamp. If 2 C of charge pass through the lamp, how much energy is transferred?
▶️ Answer/Explanation
Step 1: Energy = Voltage × Charge.
Step 2: \(E = V \times Q = 12 \times 2 = 24 \, \text{J}\).
Step 3: This 24 J is transferred to the lamp as light and heat.
Final Answer: The lamp receives 24 J of energy.
Electrical Power and Energy
Electrical Power
Power is the rate at which electrical energy is transferred or converted in a circuit.
Equation:
$ \mathrm{P = IV}$ where:
- \(\mathrm{P}\) = power (watts, W)
- \(\mathrm{I}\) = current (amperes, A)
- \(\mathrm{V}\) = potential difference (volts, V)
- 1 watt = 1 joule of energy transferred per second.
Electrical Energy
Electrical energy is the total amount of energy transferred by an electrical component over a given time.
Equation: $ \mathrm{E = IVt}$ where:
- \(\mathrm{E}\) = energy (joules, J)
- \(\mathrm{I}\) = current (A)
- \(\mathrm{V}\) = voltage (V)
- \(\mathrm{t}\) = time (s)
Everyday Applications:
- A higher-power appliance transfers energy more quickly (e.g. electric kettle vs. LED bulb).
- Electricity bills are based on electrical energy used (\(E\)), not just power.
Example :
A 60 W lamp operates from a 12 V battery. Calculate: (a) the current through the lamp, and (b) the energy transferred in 5 minutes.
▶️ Answer/Explanation
(a) Current:
Use \( \mathrm{P = IV} \). Rearr.: \(\mathrm{I = \dfrac{P}{V}} = \dfrac{60}{12} = 5 \, A\).
(b) Energy:
Use \( \mathrm{E = IVt} \). Time = 5 min = 300 s. \(\mathrm{E = 5 \times 12 \times 300 = 18{,}000 \, J}\).
Final Answer: Current = 5 A, Energy transferred = 18,000 J (18 kJ).
Kilowatt-hour (kW h)
The kilowatt-hour (kW h) is a unit of electrical energy. It is defined as the energy transferred by a device with a power of 1 kilowatt (1000 W) operating for 1 hour.
Relationship to Joules:
- 1 kW h = \(\mathrm{1000 \, W \times 3600 \, s}\)
- \(= 3.6 \times 10^6 \, \mathrm{J}\) (3.6 MJ)
- So kW h is simply a convenient large unit for household electricity usage.
Formula for Energy in kW h:
$\mathrm{Energy \ (kW h) = Power \ (kW) \times Time \ (h)}$
Calculating Electricity Cost:
Electricity companies charge for the energy used, measured in kW h. Cost is calculated as:
$\mathrm{Cost = Energy \ (kW h) \times Cost \ per \ kW h}$
Everyday Understanding:
- A 100 W bulb left on for 10 hours uses \(0.1 \, \mathrm{kW} \times 10 \, \mathrm{h} = 1 \, \mathrm{kW h}\).
- If electricity costs 20p per kW h, the cost = 20p.
Example :
A 2 kW heater is used for 3 hours each day for 30 days. Electricity costs £0.25 per kW h. Calculate the total cost.
▶️ Answer/Explanation
Step 1: Energy per day = \( \mathrm{Power \times Time = 2 \times 3 = 6 \, kW h}\).
Step 2: Energy in 30 days = \( \mathrm{6 \times 30 = 180 \, kW h}\).
Step 3: Cost = \( \mathrm{180 \times 0.25 = 45.00 \, \text{£}} \).
Final Answer: Total cost = £45.00.