1.4 The resistor

basics_resistor_picturesFigure 1.3 Some resistors

Some small facts about resistors

Resistors come in different sizes, flavors and colors. What they all have in common is that they exist of some resistive material and two leads. Electric currents can go through resistors, from one lead to the other, if a voltage is applied across the two leads.

The resistor defined

A resistor is a component for which voltage and current are proportional. In other words, the ratio of voltage over current is constant. The value of this constant is called the resistance. Or in other other words, voltage and current are linearly related. In formula form:

VR = IR.R

in which VR is the voltage across the resistor (hence the index R), IR is the current through the resistor, and R is the resistance (of the resistor). The law above is often referred to as Ohm’s Law, although this is not really correct.

Common misconception “Ohm’s Law states that V = I.R for a resistor.” No, this is not Ohm’s Law, although the formula is correct for a resistor. Georg Simon Ohm found from his experiments that for most materials, the resistance is constant over a wide range of voltages.This is rather an empirical statement about the behavior of materials. It is actually not a law at all. Again, however, engineers still refer to the above formula as Ohm’s Law, as in this e-book.

The symbol

The symbol for a resistor is shown in the figure below. Note that both current and voltage have a certain and opposite direction. There is nothing wrong in choosing the same direction, but in that case the formula should become VR = -IR.R. We’ll come back to that later.

basics_resistor_symbolFigure 1.4 Symbol of a resistor

The interpretation

First, let’s get a deeper understanding on the meaning of Ohm’s Law. This will also help in grasping the concept of voltage. Consider the current IR first. In the figure it is drawn from left to right. If the value of IR is positive, it reflects that positive charges are moving from left to right. However, this is a virtual movement, since in reality the electrons are moving from right to left in that case. The larger this current, the faster the electrons move through the resistor.

Now, travelling through a resistor requires some effort. Some external force or energy is needed to push the electrons through the resistor, and that’s where the voltage drops in. The voltage actually tells us how much energy (per unit of charge) is needed to achieve a given current through a given resistor. Ohm’s Law can be understood more intuitively now. Take these challenges:

Basics - Level 1

Take these challenges.

Basics - Level 2

A short one…

On the arrows

A final word on the voltage arrow. This arrow starts at one point and ends at another point. A voltage is always defined between two points, and it points from a point with a lower energy state to a point with a higher energy state. Everything in the real world has the tendency to evolve to a lower energy state, like water going downhill. Likewise, positive charges will tend to flow from a higher energy state to a lower one. This flow of positive charges corresponds to the direction of the current.

The current arrow has no start or end. It just indicates a direction in which the current flows. This current is the same for any point in the resistor.

Common Misconception “Isn’t it possible that a current is larger at one end of the resistor relative to the other end?” No, this is not possible. Hypothetically this would be possible if you start with an ’empty’ resistor, so without any electrons inside. In that case you would first need to ‘fill’ the resistor before a current can come out of it. However, this does not happen in the real world. Resistors consist of atoms, and atoms have electrons, so you always start with a ‘full’ resistor. Once a voltage enables an electron to go inside the resistor, another one is leaving the resistor at the other side. Neither is it possible to squeeze charges together in a smaller volume, or put more scientifically: Charges can not accumulate.

On the signs

Currents and voltages can be positive and negative. If you follow the convention of Figure 1.4 (so both arrows in opposite direction), then the voltage and the current have the same sign (so both positive or both negative). If the arrows have the same direction, then the current and the voltage have opposite sign, hence the minus sign in Ohm’s Law in that case. A negative current means that the true current flows in the other direction than the arrow indicates. Similarly, a negative voltage means that the energy or voltage drops in the direction of the arrow. The figure below represents four different representations of the same state.

basics_signs_currents_voltagesFigure 1.5 Signs of currents and voltages

Go to 1.5 Power

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