What it shows
An electric current heats a resistor, and the heat produced in a fixed time is V squared divided by R, times t. Doubling the voltage on the same coil makes it deliver four times the heat.
The science
When charge moves through a resistor, the electrical energy it loses appears as heat: H = V I t = V²t / R = I²Rt. The water gains heat Q = m c ΔT, where c is about 4200 J per kg per degree C, so ΔT = V²t / (R m c) if all the heat goes into the water. Because H depends on V squared, 3 V, 4.5 V and 6 V should give temperature rises in the ratio 4 : 9 : 16. Heat lost to the cup and the air makes the real rise a little smaller than the formula.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- About 1 m of enamelled constantan (Eureka) wire wound into a coil of 3 to 5 ohm (from an electrical shop)
- Four D cells in a holder, or a 6 V battery pack
- A small steel or plastic cup with 100 mL of water (weigh it with a kitchen scale)
- A thermometer reading to 0.5 degrees C
- A wire switch made from a clip and a pin
- A multimeter for the voltage and the current
- A phone stopwatch and a thick cloth to wrap the cup
Safety
For this project: An adult must check the coil and the connections; the coil and the cup can get hot, so never touch the coil with a bare hand while the current flows, and keep the switch off between readings. Use only cells, never mains electricity.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Wind the constantan wire on a pencil into a loose coil with the turns apart, scrape the enamel off both ends and measure the coil resistance with the multimeter.
Weigh 100 g of water into the cup, wrap the cup in cloth and stir with the thermometer until the reading is steady; note it as the start temperature.
Lower the coil into the water without letting it touch the cup wall and connect it to two cells (3 V) through the switch.
Close the switch for exactly 5 minutes, stirring gently with the thermometer, then open it and record the highest temperature seen.
Let the water cool to room temperature, replace it with fresh water and repeat with three cells (4.5 V) and then four cells (6 V).
Write a table of voltage, current, start temperature, final temperature and rise ΔT for each run.
Compute the heat gained, m c ΔT, and the electrical energy supplied, V I t, and find what percentage reached the water.
Plot ΔT against V² and check that the points lie close to a straight line through the origin.
What you should see
The graph of ΔT against V² is close to a straight line, showing that heat grows as the square of the voltage. About 60 to 90 percent of the electrical energy is found in the water; the rest warms the cup and the air.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is the formula for heat produced in a resistor?
H = I²Rt = VIt = V²t / R, in joules.
2Why does doubling the voltage give four times the heat?
The current also doubles for a fixed resistor, and heat depends on both V and I, so it grows as V squared.
3Why is the energy found in the water less than the energy supplied?
Some heat warms the cup, the thermometer and the air around it.
4Why is Eureka wire used for a heating coil?
It has high resistivity and its resistance changes very little as it warms.
Take it further
Keep the voltage fixed and use coils of two different lengths to show that heat in a fixed time is inversely proportional to R at constant voltage.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
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