Choosing Bulbs for a Solar-Powered Study Lamp
A student in Gaborone builds a study lamp powered by a small solar panel and a rechargeable battery. The panel produces 6 V and can supply a maximum current of 0.5 A in full sun. The battery stores enough energy to run the lamp for 3 hours at night. The student has three bulbs:
- Bulb X: 6 V, 0.3 A
- Bulb Y: 6 V, 0.6 A
- Bulb Z: 12 V, 0.3 A
The lamp must be bright enough to read by, must not overload the panel, and must last the whole evening. The student connects one bulb directly across the 6 V supply.
1. Calculate the power of each bulb at its rated voltage and decide which bulb(s) can safely be used with the solar panel. Show your reasoning.
Read the worked answer
Use P = V × I.
- Bulb X: P = 6 V × 0.3 A = 1.8 W; current 0.3 A is below the panel's 0.5 A limit.
- Bulb Y: P = 6 V × 0.6 A = 3.6 W; current 0.6 A exceeds the 0.5 A maximum, so it would overload the panel (and may not light fully).
- Bulb Z: rated 12 V at 0.3 A, so its resistance is R = V/I = 12/0.3 = 40 Ω. Connected to 6 V, its current would be I = V/R = 6/40 = 0.15 A, and power P = 6 × 0.15 = 0.9 W. It is safe but dim, because it is designed for a higher voltage.
Conclusion: Bulb X is the best choice - it is designed for 6 V, draws 0.3 A (within the 0.5 A limit) and gives 1.8 W. Bulb Y is unsafe for the panel; Bulb Z is safe but gives only 0.9 W, likely too dim for reading.
2. The student wants the lamp to run for 3 hours. Using Bulb X, estimate the energy needed from the battery and explain one practical way to make the lamp last longer without changing the bulb.
Read the worked answer
Energy = power × time. For Bulb X, P = 1.8 W for 3 hours = 3 × 3600 s = 10 800 s.
E = 1.8 W × 10 800 s = 19 440 J (about 19.4 kJ), or 1.8 W × 3 h = 5.4 Wh.
The battery must therefore store at least about 19.4 kJ (plus losses) to run the bulb for 3 hours.
To make the lamp last longer without changing the bulb, the student could:
- Reduce the time the lamp is on (switch off when not reading).
- Use a dimmer or resistor in series to reduce current, lowering power - though this also lowers brightness.
- Improve the battery/panel: a larger battery stores more energy; a panel that charges fully each day gives more stored energy. (This changes the power source, not the bulb.)
- Use a reflector to direct more light onto the page so a dimmer setting is still readable.
The key idea is that energy stored = power × time, so either lower the power or increase stored energy to extend running time.
3. The student notices the bulb gets warm. Explain what happens to the electrical energy and why this matters for the choice of bulb.
Read the worked answer
In a filament bulb, most electrical energy is transferred to the surroundings by heating (the filament gets hot and glows), with only a small fraction transferred as useful light. So the 1.8 W of Bulb X is not all light: a large part becomes thermal energy. This matters because:
- Less light per watt means a dimmer lamp for the same battery energy.
- Heat can damage the lamp fitting and wastes stored energy, shortening running time.
- A bulb that runs cooler (e.g. an LED designed for 6 V) would give more light for the same power, so the student should compare efficiency, not just power rating.
The warm bulb is evidence of energy transfer by heating, which is expected but undesirable in a battery-powered lamp.