When studying electric circuits, we often use Ohm’s law, which is a relationship between three related quantities. To describe materials and circuits, we need to study the current-voltage characteristics and their behaviour for different devices and setups.
What is Ohm’s law?
Ohm’s law states that:
For a conductor at a constant temperature, the current passing through it is proportional to the potential difference across it, given that physical conditions and resistance remain constant.
Or, in mathematical language:
\[V = I \cdot R\]
V is the potential difference (measured in volts, V), I is the electric current (measured in amperes, A), and R is the electrical resistance (measured in ohms Ω). This equation captures the linear relationship between the potential difference and the electric current.
But what is resistance? In short, resistance is the collective effect of a medium that obstructs the movement of charges (current). Resistance depends on many factors, such as the type of material used and the temperature of the material.
Because establishing a potential difference is relatively simple, we can generate a certain electric current by modifying the resistance. An electric current appears when we establish a potential difference between the two sides of a conductor. Because we can modify the current by changing the resistance, it is interesting to study how this resistance affects the current flow. Therefore, it is worth studying the behaviour of the resistance of materials and circuits to build devices that serve different purposes.
Ohm's law states that the relationship between the voltage in a circuit and the current flowing through it is linear and, usually, constant. It is an approximation of the behaviour of most materials.
Non-ohmic materials
Generally, resistance is not a constant obtained by dividing the potential difference by the electric current. Resistance is actually an arbitrary function R(V, I) that depends on the potential difference and the current. Ohm's law is the linear approximation for a small region of this relation. In non-ohmic materials, the resistance will not follow the linear approximation.
If we have the relation between current I and voltage V(I), we can calculate the resistance as follows:
\[R(V,I) = \frac{dV(I)}{dI}\]
Fig. 1. Linear approximation, commons.wikimedia.org
For a general function (green) that is not a straight line, we can always limit ourselves to a very small range where the relationship can be estimated by a linear relation, i.e. a straight line. The smaller the range, the better the approximation.
If the green function above captures the relationship between the voltage and the electric current, we see that for a small range where the voltage and the current do not vary a lot, the function is approximated by the red line. We can then use Ohms law to determine the resistance without needing to differentiate.
Current-voltage characteristics
Current-voltage characteristics are the curves specifying the relationship between the electric current and the potential difference of a device.
Let’s study several examples of these curves in different devices and find out what conclusions we can draw from them.
Current-voltage characteristics of an ohmic resistor
The current-voltage characteristics, also known as I-V characteristics, of ohmic resistors are:
- The I-V graph for an ohmic resistor is a straight line.
- The curve passes through the origin, which means that for zero potential difference, we have zero current.
- The current is directly proportional to the potential difference.
- The gradient is \(\frac{1}{R}\).
The I-V graph for an ohmic resistor is a straight line.
Current-voltage characteristics of a filament
Filaments are materials used in lamps that are composed of metals that glow when a certain amount of current flows through them. Filaments are a type of electric device called a thermistor, which is a material whose resistance depends on its temperature.
Since resistance is sensitive to heat and a current heats the material when it flows through it, the resistance will change. This effect is observed in the I-V curves of filaments. Technically, all materials behave in this way, but some do in a very mild scale we cannot measure.
The current-voltage characteristics of a filament lamp are:
- The I-V graph shows the current increasing at a lower rate than the potential difference (voltage).
- In ranges where the voltage is not too strong, the current is not very strong and the temperature is not very high. This means that the resistance is not high and the current can flow easily.
- In ranges where the voltage is high (positive or negative), the current generated is very strong and the temperature increases rapidly. Since the temperature increases, the resistance increases and the flow of the current decreases. For a voltage high enough, a maximum current is reached.
For filament lamps, the I-V graph shows the current increasing at a lower rate than the potential difference (voltage).
Current-voltage characteristics of a diode
A diode is a semiconductor that allows current to flow in a particular direction (but not in the opposite). It works as a conductor or a very good resistor depending on the direction of the current.
The current-voltage characteristics of diodes are:
- When the current flows in the direction that works as a conductor (positive potential difference), there is a sharp increase in the current after certain voltage values, and the resistance decreases sharply. It does so for a threshold value that determines when the diode starts conducting electricity.
- When the current tries to flow in the direction that behaves like a resistor (negative potential difference), there is approximately no current flowing. The resistance is close to infinity.
Diodes can work as a conductor or a very good resistor depending on the direction of the current.
Current-voltage characteristics of a solar photovoltaic cell
A solar photovoltaic cell is a device that converts light into electrical energy. Their functioning is based on the photoelectric effect: the release of electrons by a material when impacted by electromagnetic radiation of a certain frequency range. The higher the frequency of the light, the more intense the electric current induced.
The current-voltage characteristics of solar photovoltaic cells are a bit different because, in this case, we have control over the current generated, and our aim is to produce a potential difference.
- In the region of positive potential difference, the current can grow arbitrarily and a constant potential difference will appear. We cannot use it efficiently in this region. This is the region where the material is not receiving light.
- As the amount of incident light starts to grow, the current becomes more and more negative, and a negative potential difference appears that can grow arbitrarily depending on the characteristics of the light and the material.
I-V graphs for a resistor, diode, and battery, commons.wikimedia.org
Current-Voltage Characteristics - Key takeaways
- Ohm’s law states that the relationship between the voltage in a circuit and the current flowing through it is linear and, usually, constant. It is an approximation of the behaviour of most materials.
- The relationship between voltage and current is not linear. It is determined by the resistance, which measures the obstruction of a medium to the flow of current.
- It is helpful to study the current-voltage curves or I-V curves of different devices and materials to understand how they work.
- Diodes, filaments, and photovoltaic cells are good examples of non-ohmic devices that serve different purposes.
Explanations 
Exams 
Magazine 
