V=-N(dΦ/dt)

Electricity and Magnetism

## Model DC power line

Practical Activity for 14-16

**Class practical**

Shows the significant energy losses along any low-voltage transmission line.

Apparatus and Materials

*For each student group*

- Power line terminal rods, 2
- Retort stands and bosses, 2
- Lamps (12 V, 24 W) in lamp holders, 2
- Eureka wire, bare (28 SWG), 1.5 m, 2 lengths
- Power supply, 0 to 12 V, DC
- DC voltmeters, 2, reading to at least 12 V
- Ammeter, DC, reading to at least 2 A

Health & Safety and Technical Notes

Read our standard health & safety guidance

Procedure

- Fix two of the dowel rods, which form the power line terminals, horizontally in two bosses at a height of about 30 cm above the bench and roughly 1.5 m apart.
- Stretch two lengths of resistance wire between the terminals to form the power line.
- Connect one of the two lamps directly to the 12 volt DC supply at the
power station

end. - Connect the supply directly to one of the terminal rods.
- Connect the second lamp to the other end of the power line, where it represents the
village

. Switch on the power supply. Thevillage

lamp will just glow, in contrast with the fully-lit pilot lamp at thepower station

. - Observe the effect of connecting a second lamp in parallel with the single
village

lamp. - Connect a voltmeter in parallel with each of the lamps, and note the voltages.

Teaching Notes

- Power lines connect power stations to the consumer. This is convenient, but there is a cost to pay in energy terms. An electric current warms up the transmission cables and so there are
energy losses

as the atmosphere is warmed up. - In this model version, the wire used has significant resistance so that 1.5 m represents many km of transmission line. It is clear that energy is
lost

along the transmission wires so much so that thevillage

at the end of the transmission wires receives very little energy from thepower station

at the other end of the wire. - As well as measuring voltages, an ammeter (reading to at least 2 amp) can be connected into the supply line. Students can check that the current remains the same around the power line circuit; the current to the
power station

lamp is greater than that to thevillage

lamp. - In order to understand what is happening, students need some quantitative ideas about electricity. A current of 5 amps means a flow of charge of 5 coulombs per second. A voltmeter measures the energy. A potential difference of 3 volts means that 3 joules of energy are given to each coulomb of charge.
- Thus a volt is defined as a joule/coulomb and an ampere (amp for short) is defined as a coulomb of charge flowing per second. So with
*V*volts and*Q*coulombs, then the energy transferred is*V x Q*joules. The current is*I = Q/time*, and so the energy transferred is V x I joules per second. (A joule per second is also known as a watt, which is a measure of power.) - By measuring the current and potential difference at the power station end of the line and at the village end you can calculate the
power loss

along the line. The potential difference measured across one wire multiplied by the current in the wire will give the power loss of one wire, and so the total power loss of the wires is twice as much. This is a check on the previous calculation. The input energy should now be equal to the energy transferred to the output plus the energy transferred to warming up the transmission wires. - The heating effect of a current is proportional to the square of the current. This means that high currents and low potential differences warm up the wires more than low currents and high potential differences. Therefore, the cables transfer more energy to the environment than to the village in the high current case.
- Another way of reducing lower power losses is to reduce the resistance of the transmission lines. This is done by using wires of low resistivity such as copper or aluminium. (Silver has an even lower resistivity but it would be very expensive!) Increasing the diameter of the cable would use more copper or aluminium and that would be expensive, and they would also be heavier and so need more support.
- The efficiency of the system can be calculated from:
*efficiency = power taken by the village/power supplied at the power station*

*This experiment was safety-tested in July 2007*

A video showing this practical, plus more efficient transmission at higher voltage: