Electric circuits transfer energy from sources like electrical cells or mains supplies to components, then to the surroundings.
Example: When you switch on an electric heater, energy from a power station (possibly 100 km away) is delivered to your home and transformed into heat.
Energy is conserved in circuits: The energy provided by the power source equals the total energy transferred to components like lamps or motors.
E.g., A lamp with a potential difference (p.d.) of 1.5 V transfers 1.5 J of energy per coulomb of charge passing through it.
Electrical Power
Electrical power is the rate at which energy is transferred in a circuit.
Equation:
P = IV
P is power in watts (W), I is current in amperes (A), V is potential difference (volts).
Explanation:
1 watt = 1 joule per second (1 W = 1 J/s) .
Appliances are labeled with power ratings (e.g., 1.5 kW). These indicate the maximum energy transfer rate when operating at full power.
A label from the back of a TV. Label that shows their power rating.
Example 01:
A 12 V power supply pushes a current of 3.0 A through a resistor. At what rate is energy transferred to the resistor?
Answer:
Use of the equation P=VI
P = 12 x 3
P = 36 W (rate in energy = Power)
Example 02:
A fish tank is fitted with an electric motor, which has a power rating of 50 W. The motor is connected to a 240 V supply. What current flows through the heater when it is switched on?
Answer:
Use of the equation P=VI
given P = 50W and V = 240V find I = ?
Rearrange the equation I=PV
I=50240
I = 0.21A
Electrical Energy
Electrical energy is the total energy transferred in a circuit.
Equation:
E = IVt
E is energy in joules (J), I is current in amperes (A), V is potential difference (volts), t is time in seconds (s).
Example:
A battery stores chemical energy. The total energy it transfers is calculated using its voltage, current, and discharge time.
Example 03:
How much energy is transformed by an electric motor in an hour if a current of 40 mA flows through it when it is connected to a 120 V supply?
Answer:
Use of the equation : E = IVt
E = 0.04 x 120 x (60×60)
E = 17,280J or 17kJ
Kilowatt-hour (kWh) and Costs
An electricity meter.
The kilowatt-hour is a unit of energy commonly used to measure household electricity usage.
Definition:
1 kWh=1000 W×3600 s = 3.6×106 J.
Calculation of energy used by appliances:
Energy (kWh)=Power (kW)×Time (hours)
Energy (kWh) = Power (kW) × Time (hours)
Example:
A 2 kW heater running for 2 hours uses 4 kWh.
Cost Calculation:
Multiply energy used (kWh) by the cost per unit (e.g., 4 kWh × $0.20/kWh = $0.80).
Example 04:
Henry switches on a water motor for two hours. The power of the motor is 2.5 kW. How much energy is transferred in kWh (units)?
Answer:
Use of the equation Energy (kWh)=Power (kW)×Time (hours)
Energy = 2.5KW x 2hr
Energy = 5KWh or 5 Units
Example 05:
Phillip checks his electricity bill for a three month period. The meter reading at the start was 1541 kWh and at the end it was 1647 kWh. Electricity costs 18 cents per unit. What is his bill for electricity?
