Electrical Work & Energy
When you charge your phone, play music through a speaker, or switch on a lamp, electrical energy is being converted into other useful forms — light, sound, heat. But where does this energy come from? It comes from the work done by an electrical source, such as a battery or power supply, in pushing electric charges around a circuit. Understanding how electrical energy is delivered and calculated is fundamental to analysing any circuit, from the simplest torch to the most complex power grid. Think of a battery like a water pump in a pipe system. The pump does work to push water uphill, giving it gravitational potential energy. A battery does the analogous job: it does work on charge carriers (electrons), pushing them through the circuit and giving them electrical potential energy. As the charges flow through components like resistors or motors, this energy is transferred — converted into heat, light, motion, or sound. The battery steadily depletes its stored chemical energy as it maintains this flow. The key quantities linking electrical energy to circuit variables are voltage (potential difference), charge, current, and time. These are not isolated ideas — they combine into concise equations that let us calculate exactly how much energy a source delivers or a component consumes. Mastering these relationships unlocks the ability to design circuits, select appropriate components, and understand energy bills.
- Work done by an electric source
- Connecting charge to current and time
- Power as the rate of energy transfer
- Electromotive force (EMF) vs terminal voltage
- Conservation of energy in a circuit
Work done by an electric source
Potential difference (voltage) V between two points is defined as the work done per unit charge in moving a positive charge between those points: V = W/Q. Rearranging, the work done (electrical energy transferred) is W = QV. This is the foundational relationship: energy equals charge multiplied by voltage.
Connecting charge to current and time
Electric current I is the rate of flow of charge: I = Q/t, so Q = It. Substituting into W = QV gives W = IVt. This expresses the energy delivered by a source (or consumed by a component) in terms of current, voltage, and time — three quantities that are easy to measure with ammeters and voltmeters.
Power as the rate of energy transfer
Power P is the rate at which energy is transferred: P = W/t. From W = IVt it follows that P = IV. This is the electrical power equation. Combined with Ohm's law (V = IR), alternative forms arise: P = I²R and P = V²/R. These allow power to be found from any two of V, I, R.
Electromotive force (EMF) vs terminal voltage
A real battery has an internal resistance r. Its electromotive force (EMF) ε is the total energy supplied per unit charge. When current flows, some energy is wasted internally: the terminal voltage V = ε − Ir. Thus the energy delivered to the external circuit per unit charge is less than ε. The total energy supplied by the source is W = εQ = εIt, while the useful energy delivered externally is W_ext = VQ = VIt.
Conservation of energy in a circuit
Energy is conserved in every circuit. All the electrical energy supplied by sources equals all the energy dissipated or stored in components. This is Kirchhoff's Voltage Law viewed through an energy lens: the sum of EMFs around a loop equals the sum of potential drops. No energy is created or destroyed — it is only converted between forms.
The Key Equation
- W — Electrical energy (work done) (Joule (J)): The total electrical energy transferred by the source or consumed by a component.
- Q — Electric charge (Coulomb (C)): The total charge that flows through the component or is moved by the source.
- V — Potential difference (voltage) (Volt (V)): The energy transferred per unit charge; for a source this is the terminal voltage or EMF.
- I — Current (Ampere (A)): The rate of flow of charge through the circuit.
- t — Time (Second (s)): The duration for which the current flows.
Worked Example
Problem. A 12 V car battery delivers a current of 2.5 A to the headlights for 30 minutes. (a) Calculate the total electrical energy delivered by the battery. (b) If the battery has an internal resistance of 0.4 Ω, calculate the energy wasted inside the battery during this time.
Answer. The battery delivers 54 kJ of electrical energy in total; 4.5 kJ of that is wasted as heat inside the battery due to its internal resistance, leaving 49.5 kJ available to the headlights.
Origins · 1 minJames Prescott Joule and how this was discovered
Joule established the quantitative relationship between electrical current and heat produced — now known as Joule's law (P = I²R) — and experimentally demonstrated the equivalence of mechanical work, heat, and electrical energy. His meticulous experiments underpinned the law of conservation of energy and established that electrical energy is measured in the unit now named after him, the joule (J). Joule was so obsessed with precision that he reportedly carried a thermometer on his honeymoon to measure the temperature difference between the top and bottom of a waterfall — testing his theories about mechanical energy converting to heat.
Related Concepts
- Potential Difference & Voltage — Voltage (potential difference) is the energy per unit charge and appears directly in W = QV, making it inseparable from the concept of electrical energy.
- Electrical Power — Power P = IV is the rate of energy transfer; understanding electrical energy naturally leads to calculating how quickly that energy is delivered or consumed.
- Electric Current & Charge — Current and charge are the carriers of electrical energy; the relation Q = It links charge flow directly to the energy equation W = IVt.
- EMF & Internal Resistance — The EMF of a source defines the total electrical energy supplied per unit charge, while internal resistance determines how much energy is wasted inside the source.