A-level Physics (Advancing Physics)/Power/Worked Solutions

1. The potential difference across a 9W light bulb is 240V. How much current is flowing through the light bulb?

9 = 240I

$I=\frac{9}{240}=0.0375\text{ A}$

2. How much energy is dissipated by a 10W component in 1 hour?

$10=\frac{E}{60^2}$

E = 60² x 10 = 36000 J = 36 kJ

3. The potential difference across a top-notch kettle, which can hold up to 1 litre of water, is 240V, and the current is 12.5 A. 4.2 kJ of energy is required to heat a litre of water to 100°C. Assuming 100% efficiency, how long does it take to boil 1 litre of water?

$12.5\times 240=3000=\frac{4.2\times 10^3}{t}$

$t=\frac{4.2\times 10^3}{3000}=1.4\text{ s}$

The reason this is unrealistically small is that kettles are not 100% efficient as they lose lots of heat into the air surrounding the kettle.

4. How much energy is dissipated by a 100Ω resistor in 10 seconds if 2A of current are flowing?

$\frac{E}{10}=2^2\times 100=400$

E = 4000 J = 4 kJ

5. The charge on an electron is -1.6 x 10^-19 C. How long does it take for a mole (6 x 10²³ particles) of electrons to flow through a 40W light bulb on a 240V ring main?

Total charge = 1.6 x 10^-19 x 6 x 10²³ = 96000 C

$40=\frac{96000\times 240}{t}=\frac{23040000}{t}$

$t=\frac{23040000}{40}=576000\text{ s}=9600\text{ min}=160\text{ h}=6\text{ days }16\text{ hours}$