Efficiency Calculations

$$\text{efficiency}=\frac{E_{\text{useful}}}{E_{\text{total}}}\times 100\%P=VIE=Pt$$

1. A motor is supplied $500\mathrm{J}$ and delivers $425\mathrm{J}$ of motion. Find its efficiency and the energy wasted.

Answer

$\frac{425}{500}\times 100\%=85\%$, with $75\mathrm{J}$ wasted — mostly as heat in the windings, some as sound.

2. A bulb converts $1200\mathrm{J}$ into $60\mathrm{J}$ of light. Efficiency? What became of the rest?

Answer

$\frac{60}{1200}\times 100\%=5\%$. The other $1140\mathrm{J}$ became heat. An incandescent bulb is a space heater that happens to glow.

3. A $1500\mathrm{W}$ kettle runs for 3 minutes. How much energy, in joules and in kilowatt-hours?

Answer

$E=(1500\mathrm{W})(180\mathrm{s})=270000\mathrm{J}$

In kilowatt-hours: $1.5\mathrm{kW}\times 0.05\mathrm{h}=0.075\mathrm{kWh}$

4. At $0.13\text{textdollar}/kWh$, what does question 3 cost?

Answer

$0.075\mathrm{kWh}\times 0.13\approx \text{textdollar}0.01$ — about one cent. Worth knowing before anyone tells you the kettle is why the bill is high.

5. A 60 W incandescent bulb and a 9 W LED give the same light. Over 1000 hours, how much energy does each use, and what is saved?

Answer

Incandescent: $60\mathrm{kWh}$. LED: $9\mathrm{kWh}$. A saving of $51\mathrm{kWh}$, or about $6.63 at 13 cents.

One bulb, one year of evenings. Multiply by every socket in a school.

6. A solar panel receives $1000W/{\mathrm{m}}^2$ and produces $200W/{\mathrm{m}}^2$. Efficiency? Where does the rest go?

Answer

$20\%$. The rest is reflected, passes straight through, or becomes heat in the panel — which is itself a problem, because a hot panel is a less efficient one.

Reference: Electrical Power and Efficiency