Heat, Power and Energy at Home: Quick Revision

A brief note on Heat, Power and Energy at Home. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• Joule's law: $H = I^2 R t = VIt = \dfrac{V^2}{R}\,t$. Double the current, four times the heat.
• Power: $P = VI = I^2 R = \dfrac{V^2}{R}$, in watts. A rating such as $220\ \text{V}$, $60\ \text{W}$ holds only at that voltage.
• Energy $E = Pt$. One unit is $1\ \text{kWh} = 3.6 \times 10^{6}\ \text{J}$; units $=$ kW $\times$ hours.
• The bill $=$ units $\times$ price of one unit.
• A fuse in the live wire melts when the current is too large.

The facts at a glance

A worked example

A $2.4\ \text{kW}$ water heater runs $40$ minutes a day for $30$ days. One unit costs $7$ rupees. Find the units and the cost.

1. Each day. $2.4\ \text{kW} \times \dfrac{40}{60}\ \text{h} = 1.6\ \text{kWh}$.
2. The month. $1.6\ \text{kWh} \times 30 = 48\ \text{kWh}$.
3. The cost. $48 \times 7$ rupees $= 336$ rupees.

Practice with new numbers

A program to try

The program finds the current, the resistance and the monthly units of one appliance.

Mistakes to avoid

• Forgetting to square the current in $H = I^2Rt$ or $P = I^2R$.
• Mixing watts and kilowatts. Units need kW and hours.
• Using minutes as hours. $40$ minutes is $\dfrac{2}{3}$ of an hour.
• Choosing a fuse far above the normal current. It must melt before the wires overheat.

Check yourself

1. A current of $0.8\ \text{A}$ flows through $50\ \Omega$ for $2$ minutes. How much heat is produced?

2. An appliance takes $2.2\ \text{A}$ from $230\ \text{V}$. What is its power?

3. A $750\ \text{W}$ iron is used for $3$ hours. How many units does it use?

4. A $2000\ \text{W}$ iron runs on $220\ \text{V}$. What current does it take?