POWER AND ENERGY IN CIRCUITS
We have assumed that energy is entirely equivalent to voltage in our raft idea but a little reflection will point out that this is daft and wrong. The more electrical heaters we turn on in winter will not change the voltage, but will increase the current because more things need current through them. Clearly more energy is being transferred from the generator to your house, witness your temperature and Mum and Dad’s bill!
We defined potential difference or voltage to be the energy per coulomb. This is where the current enters, through considering how many coulombs are driven in time. In our raft analogy, we can have faster (or slower) rafts on our white water circle. As each undergoes the circuit, each acquires, then loses energy, so the more involved, the more energy acquired or lost. As more current is involved, more electrons gain and lose energy.
We can convert these ideas into a set of formulae.
Think of a section of conductor such as a radiator. It will have a current through it, I, responding to resistance R, under a potential difference of V. Energy change will take place in the radiator ( there is a change in potential energy).
Potential Difference = Energy change
V = Energy change ( definition )
charge passing
q
but, Current I = Charge passing
I = q/t
time
substituting for q, the charge passing,
V = Energy change
It
thus the energy change in the section of conductor,
Energy change = VIt in joules, V is PD across the conductor,
I is the current through the conductor
variations on this using V= IR are, Energy Change = I2Rt = V2 t /R
eg A 3 amp current passes through a radiator which has 240 volt across it for 50 seconds. How much energy is changed in the radiator ( presumably to heat )?
Soln. Energy Change in the radiator is = VIt = 240x3x50 joules
= 36000 = 3.6 x 104J
Power "used" in a section of conductor
Power is the rate of energy change. The quicker the energy change takes place, then the more "powerful" the thing is. ( Compare someone digging a garden to a small rotary hoe digging the same garden - which is more powerful?)
The formula connecting the two ideas is
power = Energy change
thus Pt = Energy change
time taken
So using this on the above formulae for energy change
Energy change = VIt = Pt
finally P
= VI ( = I2R = V2 /R ), measured in watts
This explains "60W" lamps etc in the home. Under normal conditions of usage, ie in a 240 V socket, 60 joules each second of heat /light energy is created from electrical energy.
eg
For the above lamp, how much current is flowing when it is on?
Solution; Under normal usage, V=240 volts, I = ?, P = 60watts , so using the above formula,
P =VI
60 = 240 x I
so, I = 60/240 = 0.25 amps
Similarly, heaters designed for Australia are rated up to 2.4 kW meaning that they call on 10A from the household mains.
Please note that other countries do not necessarily use 240V. England does, as do many countries belonging to the old British Empire, but USA and Japan operate at 110V. If you go overseas, don’t try to use your personal electric razors or whatever without knowing the local system nor buy electrical devices in the expectation that you can use them here.
eg
A local 60W mains device has a resistance given
by P = V2/R , so R = 240 2/60
ohms. This equals 960 ohms.
Plugged into the US mains, it will try to operate
at P = 1102/960 = 12.6 watt. It won’t work
and probably do permanent damage to any motors in the device.
Electronic circuits operate at much lower potential differences, typically 5 to 9 volts, so the components are given a maximum power rating, typically up to 1/8 watt, though higher values may be used for "heavy duty" circuits. A Pentium chip operates at a power of about 20 watt and needs cooling fins. If a component has too high a current through it (too high a voltage placed across it), it overheats. This overheating destroys the crystals or whatever and the component fails, usually catastrophically and the whole circuit dies.