Electrical energy and electrical power Revision Notes

An electric circuit is a closed loop that allows electric charge to flow continuously. The circuit includes a source of electrical energy, such as a battery or mains supply, and components like resistors, bulbs, or motors.

The primary function of an electric circuit is to transfer energy from the source to the components. Electrical energy is carried by moving charges (electrons) through the circuit.

Energy is conserved in the circuit: the electrical energy supplied by the source is converted by components into other forms of energy, such as light, heat, or mechanical energy, which is then transferred to the environment.

• Electric circuits form a closed path for charge flow.
• Energy flows from the source to components via the circuit.
• Energy conversion occurs within components, transferring energy to the environment.

The two common sources of electrical energy in circuits are batteries and mains electricity.

A battery converts chemical energy into electrical energy, providing a potential difference that drives current around the circuit.

Mains electricity is supplied from power stations and delivered through the national grid; it provides electrical energy at a fixed potential difference (e.g., 230 V in the UK).

• Battery: chemical energy → electrical energy.
• Mains supply: electrical energy from power stations.
• Both provide potential difference to drive current.

Components in a circuit convert electrical energy into other useful forms:

A bulb converts electrical energy into light and heat energy.

A resistor converts electrical energy mainly into heat energy (Joule heating). This is due to collisions between moving electrons and atoms in the resistor material, causing energy transfer to thermal energy stores of the resistor and surroundings.

• Electrical energy is converted to light, heat, or mechanical energy.
• Energy conversion depends on the component type.
• Energy is transferred to the environment as heat or light.

Electric current is the flow of charge, but current itself is not used up; it is the energy carried by the charges that is transferred.

The source supplies energy to each coulomb of charge, giving it electrical potential energy.

As charges pass through components, this electrical potential energy is converted into other energy forms, which then leave the circuit to the environment (e.g., light radiated from a bulb).

• Current is charge flow rate, not energy flow.
• Energy per coulomb is given by potential difference (voltage).
• Energy is conserved: electrical energy → other energy forms.

To illustrate energy transfer, draw a simple circuit diagram with a battery, connecting wires, and a bulb.

Label the battery as the energy source supplying electrical energy.

Indicate the flow of energy from the battery through the wires to the bulb, where electrical energy is converted to light and heat energy, which is then transferred to the surroundings.

• Draw battery, wires, and bulb in a closed loop.
• Label energy flow from battery to bulb.
• Show energy conversion and transfer to environment at bulb.

Electrical power is the rate at which electrical energy is transferred or converted in an electrical circuit. It tells us how much energy is used or supplied per unit time.

Power is a scalar quantity measured in watts (W). One watt is defined as one joule of energy transferred per second (1 W = 1 J/s).

In electrical circuits, power indicates how quickly electrical energy is being converted into other forms such as heat, light, or mechanical energy.

• Power (P) is the rate of energy transfer.
• Unit of power: watt (W).
• 1 watt = 1 joule per second (1 W = 1 J/s).

The electrical power in a circuit component can be calculated using the formula:

P = IV, where: I is the current in amperes (A), V is the potential difference across the component in volts (V), and P is the power in watts (W).

This formula arises because current (I) is the rate of flow of charge, and voltage (V) is the energy transferred per unit charge. Multiplying these gives energy per unit time, which is power.

• P = IV (Power = Current × Voltage)
• I in amperes (A)
• V in volts (V)
• P in watts (W)

To calculate electrical power, substitute the known values of current and voltage into the formula.

Example: If a device draws a current of 2 A at a potential difference of 12 V, the power is:

P = IV = 2 A × 12 V = 24 W. This means the device uses energy at a rate of 24 joules per second.

• Write down the formula: P = IV
• Substitute values with units: P = 2 A × 12 V
• Calculate: P = 24 W
• Include units in the final answer

A frequent mistake is to confuse units or omit them, leading to incorrect answers.

Another error is mixing up current and voltage values or using incorrect units (e.g., milliamperes without conversion).

Always check that current is in amperes and voltage in volts before calculating power.

• Always use amperes for current and volts for voltage.
• Convert milliamperes (mA) to amperes by dividing by 1000.
• Include units in every step to avoid confusion.
• Double-check substitutions before calculating.

To illustrate electrical power, draw a simple circuit with a battery, a resistor, and an ammeter and voltmeter.

Draw a rectangle to represent the battery with '+' and '−' signs to indicate polarity.

Connect a resistor symbol (a zigzag line) in series with the battery and an ammeter (circle with 'A') to measure current flowing through the resistor. Place the ammeter in series with the resistor and battery circuit path. Attach a voltmeter (circle with 'V') in parallel across the resistor to measure potential difference.

• Battery symbol with polarity signs.
• Resistor symbol in series.
• Ammeter in series to measure current.
• Voltmeter in parallel across resistor to measure voltage.

Electrical energy transferred in an electric circuit is the amount of energy converted from electrical energy into other forms, such as heat, light, or mechanical energy, by components in the circuit.

The energy transferred depends on the current flowing through the circuit, the potential difference across the component, and the time for which the current flows.

The fundamental formula relating these quantities is: E = IVt, where E is the electrical energy transferred, I is the current, V is the potential difference, and t is the time.

• E = electrical energy transferred (joules, J)
• I = current (amperes, A)
• V = potential difference (volts, V)
• t = time (seconds, s)

Electrical energy transferred is the work done by the electric current in moving charge through a potential difference.

The charge Q passing through the circuit in time t is given by Q = It, where I is current and t is time.

The work done (energy transferred) in moving charge Q through potential difference V is E = QV. Substituting Q = It gives E = V × I × t, or E = IVt.

• Charge Q = It (coulombs, C)
• Energy transferred E = QV (joules, J)
• Substitution leads to E = IVt

The units of each quantity must be consistent to correctly calculate electrical energy transferred.

Current I is measured in amperes (A), potential difference V in volts (V), time t in seconds (s), and energy E in joules (J).

One joule is one watt-second, so electrical energy can also be expressed in watt-seconds (W·s). For larger amounts of energy, kilowatt-hours (kW·h) are used, but this is beyond the scope of this objective.

• 1 A = 1 coulomb per second
• 1 V = 1 joule per coulomb
• 1 J = 1 watt × 1 second
• Ensure time is in seconds for E = IVt

Calculate the electrical energy transferred when a current of 3.0 A flows through a component with a potential difference of 12 V for 5 minutes.

Step 1: Write down the formula: E = IVt. Step 2: Convert time to seconds: 5 minutes = 5 × 60 = 300 s. Step 3: Substitute values: E = 3.0 A × 12 V × 300 s. Step 4: Calculate: E = 10800 J. Step 5: State the answer with units: The electrical energy transferred is 10800 joules (J).

• Convert time to seconds before substitution
• Multiply current, voltage and time
• Include units in final answer

A frequent mistake is to use time in minutes or hours without converting to seconds, leading to incorrect energy values.

Another error is confusing power (P = IV) with energy; power is the rate of energy transfer, while energy is power multiplied by time.

Always check units carefully and ensure consistent use of amperes, volts, and seconds in calculations.

• Always convert time to seconds for E = IVt
• Do not confuse power (watts) with energy (joules)
• Check units at each step to avoid errors

The kilowatt-hour (kWh) is a unit of energy commonly used to measure electrical energy consumption. It represents the amount of energy transferred or used when a device with a power rating of one kilowatt (1 kW) operates continuously for one hour (1 h).

Since power is the rate of energy transfer, energy (E) can be calculated by multiplying power (P) by time (t):

\[ E = P \times t \] where: E is energy in joules (J), P is power in watts (W), and t is time in seconds (s). However, because electrical energy consumption is often large, the kilowatt-hour is used as a practical unit: 1 kWh = 1000 W × 3600 s = 3,600,000 J (3.6 MJ).

• 1 kilowatt-hour (kWh) = energy used by a 1 kW device running for 1 hour.
• 1 kWh = 3.6 × 10⁶ joules (J).

To find the electrical energy consumed by an appliance, multiply its power rating by the time it is used, then convert to kilowatt-hours if necessary.

Formula: \[ \text{Energy (kWh)} = \frac{\text{Power (W)} \times \text{Time (hours)}}{1000} \]

Example: A 500 W heater used for 3 hours consumes: \[ \frac{500 \times 3}{1000} = 1.5 \text{ kWh} \]

• Convert power from watts to kilowatts by dividing by 1000.
• Ensure time is in hours for kWh calculation.
• Multiply power (kW) by time (h) to get energy (kWh).

Electricity suppliers charge consumers based on the amount of energy used, measured in kilowatt-hours. The cost is calculated by multiplying the energy consumed by the price per kilowatt-hour.

Formula: \[ \text{Cost} = \text{Energy (kWh)} \times \text{Price per kWh} \]

Example: If the price is 15 pence per kWh and a device uses 2 kWh, the cost is: \[ 2 \times 15p = 30p \]

• Know the unit price of electricity (pence or cents per kWh).
• Multiply energy consumed by unit price to find total cost.

A 1000 W (1 kW) electric kettle is used for 0.5 hours. The electricity price is 20 pence per kWh. Calculate the energy used and the cost.

Step 1: Calculate energy used: \[ E = P \times t = 1 \text{ kW} \times 0.5 \text{ h} = 0.5 \text{ kWh} \]

Step 2: Calculate cost: \[ \text{Cost} = 0.5 \text{ kWh} \times 20p/\text{kWh} = 10p \]

• Always convert power to kilowatts and time to hours before calculation.
• Multiply energy by unit price for cost.
• Common error: forgetting to convert watts to kilowatts or minutes to hours.

Electricity bills show total energy consumption in kWh and the corresponding cost. Understanding kWh helps consumers manage usage and expenses.

To reduce costs, use lower power devices or reduce usage time.

When comparing appliances, consider both power rating and typical usage duration to estimate energy consumption and cost effectively.

• Energy consumption depends on power and usage time.
• Lower power or shorter use reduces energy and cost.
• Check appliance labels for power ratings to estimate consumption.