IMAT Physics · Electricity

Electrical Power, Energy and the Effects of a Current

Electrical power is the energy transferred each second, P = VI; over time it adds up to energy, often counted in kilowatt-hours.

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Why this matters

The 2017 paper asked for the power in a resistor from its resistance and current, and the 2024 ministry paper ran the same formula backwards to find a resistance. The 2012 paper asked which effects of a current remain in a superconductor.

Concept 1 of 3: Electrical power: P = VI = I²R = V²/R

Each coulomb crossing a p.d.

V

hands over

V

joules, and

I

coulombs cross every second. So the energy per second is

V

times

I

. Ohm's law then lets you swap

V

I

for whatever the question gives you.

Definition

Power is the rate of energy transfer, in watts ( $1\ \text{W} = 1\ \text{J/s}$ ).

For any component: $P = VI$ .
For a resistor, using $V = IR$ : $P = I^2 R = V^2/R$ .
Choose the form that uses what you are given: $I^2 R$ when the current is known, $V^2/R$ when the voltage is known.
In a resistor all of this power becomes heat (Joule heating).

Electrical power

P = VI = I^2 R = \frac{V^2}{R}

$P$ power, in W
$V$ p.d. across the component, in V
$I$ current through it, in A
$R$ resistance, in Ω

Worked example

A kettle rated 2.3 kW runs on a 230 V supply. Find the current it draws and its resistance.

Practice this conceptself-check · 3 quick reps

Doubling the current quadruples the power

In a fixed resistor

P = I^2 R

, so the power goes with the square of the current. Doubling the current multiplies the heating by 4, not 2. The options often include the result of forgetting the square.

Concept 2 of 3: Electrical energy and the kilowatt-hour

Power tells you how fast energy is used; leave the appliance on longer and the energy adds up. Joules are tiny for household use, so electricity bills count energy in kilowatt-hours: one kilowatt running for one hour.

Definition

Energy transferred: $E = Pt = VIt$ . Since $Q = It$ , this is also $E = QV$ .
The kilowatt-hour (kWh) is a unit of energy: $1\ \text{kWh} = 1000\ \text{W} \times 3600\ \text{s} = 3.6 \times 10^6\ \text{J}$ .
To use kWh, put the power in kilowatts and the time in hours.
Cost = energy in kWh × price per kWh.

Electrical energy

E = P t = V I t \qquad 1\ \text{kWh} = 3.6 \times 10^6\ \text{J}

$E$ energy, in J (or kWh)
$P$ power, in W (or kW)
$t$ time, in s (or h)

Worked example

A 2.0 kW heater runs for 3.0 hours. Find the energy used in kWh and in joules, and the cost at €0.25 per kWh.

Practice this conceptself-check · 3 quick reps

The kilowatt-hour is energy, not power

A kWh is a kilowatt multiplied by an hour, so it measures energy, like the joule. Mixing watts with hours, or kilowatts with seconds, gives answers off by factors of 1000 or 3600.

Concept 3 of 3: The three effects of an electric current

A current can heat the conductor, make a magnetic field around it, and, in a liquid with ions, cause chemical change. These effects have different causes, so they do not always come together. The magnetic effect is the one that never goes away, because every moving charge makes a magnetic field.

Definition

Heating (thermal) effect: moving charges collide with the ions of the conductor and give them energy. It needs resistance, so it vanishes in a superconductor.
Magnetic effect: every current produces a magnetic field around it, whatever the conductor. It is present even with zero resistance; strong magnets (such as those in MRI scanners) use superconducting coils.
Chemical effect: in an electrolyte the moving ions are discharged at the electrodes (electrolysis). A solid metal carries current by electrons only, so no chemical change happens in it.

Effect	Cause	Uses	In a superconducting wire?
Heating	Charges colliding with the conductor's ions	Kettles, toasters, fuses, filament lamps	Absent (zero resistance)
Magnetic	Any moving charge	Electromagnets, motors, relays, MRI scanners	Present
Chemical	Ions discharged at electrodes	Electrolysis, electroplating, charging batteries	Absent (no ions move in a solid metal)

Practice this conceptself-check · 3 quick reps

Zero resistance does not remove the magnetic effect

A superconductor has no resistance, so it produces no heat. It still produces a magnetic field, because the field comes from the moving charge, not from the resistance. That is exactly why superconducting coils make the strongest electromagnets.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Electrical power: P = VI = I²R = V²/R
Electrical power
$P = VI = I^2 R = \frac{V^2}{R}$
Electrical energy and the kilowatt-hour
Electrical energy
$E = P t = V I t \qquad 1\ \text{kWh} = 3.6 \times 10^6\ \text{J}$

Reference tables (1)

The three effects of an electric current3 rows

Effect	Cause	Uses	In a superconducting wire?
Heating	Charges colliding with the conductor's ions	Kettles, toasters, fuses, filament lamps	Absent (zero resistance)
Magnetic	Any moving charge	Electromagnets, motors, relays, MRI scanners	Present
Chemical	Ions discharged at electrodes	Electrolysis, electroplating, charging batteries	Absent (no ions move in a solid metal)

Watch out for (3)

Doubling the current quadruples the power
→ Electrical power: P = VI = I²R = V²/R
The kilowatt-hour is energy, not power
→ Electrical energy and the kilowatt-hour
Zero resistance does not remove the magnetic effect
→ The three effects of an electric current

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