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

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

9 = 240I

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

2. How much energy is dissipated by a 10 W 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 240 V, and the current is 12.5 A. 4.2 kJ of energy is required to raise the temperature of 1 kg of water by 1C. Assuming 100% efficiency and the temperature has to be raised 80K (20C to 100C), how long does it take to boil 1 litre of water?

$12.5\times 240=3000={\frac {4.2\times 10^{3}\times 80}{t}}$

$t={\frac {4.2\times 10^{3}\times 80}{3000}}=112{\mbox{ s}}$

In practice it may take longer than this as energy will be lost heating the surrounding air, heating the materials used in the kettle and the water may be colder than 20C.

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 40 W light bulb on a 240 V circuit?

Total charge = 1.6 x 10⁻¹⁹ x 6 x 10²³ = 96000 C

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

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