Resistors are components which obey Ohm's Law. When we apply various voltages we get results of the kind indicated in figure 2.1. This result shows that the current, I, is proportional to the applied voltage, V. This allows us to define a value for the resistance, , of the piece of material. Once we know this value we can predict what current any other voltage will produce. The equation and its re-arranged forms, & are all regarded as forms of “Ohm's Law” which tells us that the current will always vary in proportion with the voltage for a given piece of material.
When we apply a voltage, V, between the leads of a resistor we can expect a current, to flow through it. The way the electrons move through the solid material is a bit like the way a gas diffuses through a sponge or toothpaste squeezes along a tube. The electrons keep being accelerated by the applied electric field. This means they acquire some kinetic energy as they move towards the +ve end of the piece of material. However, before they get very far they collide with an atom and lose some of their kinetic energy. This keeps happening. As a result they tend to ‘drift’ towards the +ve end, bouncing around from atom to atom on the way. This process is illustrated in figure 2.2.
This process of drifting or diffusing is why the material obeys Ohm's Law. The average drift velocity is proportional to the applied electric field. Hence the current we get is proportional to the applied voltage. It also explains why we have to supply energy to maintain the current. We have to give the electrons kinetic energy to move them along. This keeps being ‘lost’ every time they interact with an atom. Of course, the kinetic energy doesn't really vanish. It is given to the atoms, making them jiggle around more furiously — i.e. it warms up the resistor. As a result, electrical energy is turned into heat.
The rate of energy loss or the power dissipation , P, in the resistor can be calculated from . This equation makes sense since we can expect a higher voltage to make the electrons speed up more swiftly, hence they have more energy to lose when they strike an atom. Double the voltage would double the rate at which each electron picks up kinetic energy and loses it again by banging into the atoms. The current we get at any particular voltage depends upon how many ‘free’ electrons there are, able to move in response to the applied field. Twice the number of electrons would give us twice the current. It also means twice as many electrons requiring kinetic energy to move them and colliding with atoms. So, the rate at which the resistor ‘eats’ electrical energy and converts it into heat is proportional to the voltage and the current. i.e. the power dissipation (rate of energy loss) is .
When we know the value of the resistor we don't have to know both the current and the voltage to calculate the power dissipation. We can use Ohm's Law to replace either the voltage or current in the above expression to produce the result . From this result we can see that the rate of energy loss varies with the square of the voltage or current. When we double the voltage applied to a resistor the rate at which we supply it with energy get four times bigger. This behaviour occurs because increasing the voltage also makes the current rise by the same amount.
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