2. Electrical Power and Energy#
Electrical energy is produced or consumed whenever current flows through a component or circuit.
It represents the conversion of electrical energy into another form (heat, light, mechanical work, etc.).
2.1 Electrical Work (Energy)#
Whenever an electric current flows through a conductor or a device, electrical work is performed.
The amount of work is directly proportional to the voltage, current, and time.
Formula:
$$ W = U \times I \times t = Q \times U $$Since \( Q = I \times t \):
$$ W = U \times I \times t $$Unit:
\([W] = \text{V·A·s} = \text{Ws} = \text{Joule (J)}\)
2.2 Electrical Power#
Power describes the rate at which energy is converted.
Formula:
$$ P = \frac{W}{t} = U \times I $$Unit:
\([P] = \text{V·A} = \text{Watt (W)} = \text{J/s}\)
2.3 Derived Power Formulas (using Ohm’s Law)#
By substituting \( U = R \times I \) or \( I = U / R \), additional relationships can be derived:
$$ P = U \times I \\ P = \frac{U^2}{R} \\ P = I^2 \times R $$and accordingly for electrical work:
$$ W = U \times I \times t \\ W = \frac{U^2}{R} \times t \\ W = I^2 \times R \times t $$2.4 Practical Unit — Kilowatt‑Hour (kWh)#
In practical applications, electrical energy is often expressed in kilowatt‑hours (kWh):
$$ 1\,\text{kWh} = 1000\,\text{W·h} = 1000 \times 3600\,\text{Ws} = 3.6 \times 10^6\,\text{J} $$Therefore:
$$ 1\,\text{kWh} = 3.6 \times 10^6\,\text{J} $$2.5 Thermal Effect (Joule Heating)#
When current flows through a resistor, the electrical energy is converted into heat.
From Ohm’s Law:
If \( R \) is constant:
$$ P = U^2 / R = I^2 \times R $$and for the energy released over time:
$$ W = (U^2 / R) \times t = I^2 \times R \times t $$This principle is applied in electric heaters, incandescent lamps, and fuses.
2.6 Example Calculations#
Example 1 — Power Consumption:
A lamp operates at 230 V and draws 0.5 A. Determine the power.
Example 2 — Energy Consumption:
The same lamp runs for 5 hours. Determine the energy used.
Example 3 — Heating Wire:
A resistor with \( R = 20\,\Omega \) is connected to \( U = 10\,\text{V} \).
Determine the current and the power.
💡 Summary:
Electrical power quantifies the rate at which electrical energy is converted.
Using Ohm’s Law, voltage, current, and resistance can be used to calculate energy consumption and losses in any component or circuit.