Electric Power
Introduced| English | Meaning |
|---|---|
| electric power/ɪˈlektrɪk ˈpaʊə/ | electric power |
| watt/wɒt/ | The SI unit of power, equal to one joule per second. |
Why a heater glows and a wire stays cool
- A toaster's element glows red-hot, yet the cord feeding it barely warms.
- Both carry the same current — but the element dissipates far more energy per second.
- The rate at which a component turns electrical energy into heat or light is electric power 电功率.
- Getting the power formulas straight lets you size heaters, bulbs and fuses.
Power in a circuit
- Electric power is the rate of energy transfer: $P = IV$ (current times voltage).
- Its unit is the watt 瓦特, as in mechanics ($1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$).
- Every second, a component converts $P$ joules of electrical energy into another form.
- For a resistor that "other form" is heat; for a bulb, heat and light.
Voltage, current and power
Change the voltage and resistance and watch the current and dissipated power respond.
A bulb carries $0.5\ \text{A}$ at $12\ \text{V}$. What power does it dissipate, in watts?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
$P = IV = 0.5 \times 12 = 6\ \text{W}$.
Electric power is measured in ____.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
$1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$.
Three forms of the same law
- Combine $P = IV$ with Ohm's law $V = IR$ to get two more useful forms.
- $P = I^2 R$ — handy when you know the current and resistance.
- $P = \dfrac{V^2}{R}$ — handy when you know the voltage and resistance.
- All three give the same power; pick whichever fits your known quantities.
A current of $2\ \text{A}$ flows through a $3\ \Omega$ resistor. What power is dissipated, in watts?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
$P = I^2R = 2^2 \times 3 = 12\ \text{W}$.
You know a resistor's current and resistance. Which power formula is most direct?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
$P = I^2R$ uses exactly the current and resistance you know.
Select all correct expressions for electric power.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
The first three are equivalent power formulas. $I/V$ is not power.
Energy used over time
- Power is energy per second; total energy used is $E = Pt$.
- This is what electricity meters measure and what you pay for.
- A high-power device left on briefly can use less energy than a low-power one left on for hours.
- Fuses are rated by the current (and so the power) a wire can safely carry.
A $6\ \text{W}$ bulb is left on for $10\ \text{s}$. How much energy does it use, in joules?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
$E = Pt = 6 \times 10 = 60\ \text{J}$.
Watch which power formula fits your data. $P = I^2R$ uses current and resistance; $P = V^2/R$ uses voltage and resistance. Plugging voltage into the $I^2R$ form (or current into $V^2/R$) is a common slip.
A bulb carries $0.5\ \text{A}$ at $12\ \text{V}$. What power does it dissipate?
- $P = IV = 0.5 \times 12 = 6\ \text{W}$.
Left on for $10\ \text{s}$, it uses $E = Pt = 6 \times 10 = 60\ \text{J}$ of energy.
Electric power is the energy transferred per second: $P = IV = I^2R = \dfrac{V^2}{R}$ (in watts). A resistor turns it into heat. Total energy used is $E = Pt$ — what electricity meters measure. Pick the power form that matches your known quantities.
Write from a power of 20 W
- A heater carries 4 A at 5 V.
- Find the power, and the energy used in 8 s.
A heater carries 4 A at 5 V. What power does it dissipate, in watts, and how much energy does it use in 8 s, in joules?
4 times 5 is 20. 20 times 8 is 160.
How much energy does the heater use in 8 s?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Power times time is 160 J. Other options — 60 J (the lesson bulb); 20 J (the power used as the energy).