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Current-Voltage Characteristics

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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.

First off, what is Ohm’s law?

Ohms law states:

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 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:

If the relation between the voltage and the current is of linear proportionality, i.e. V=k·I, the derivative shows that the constant of proportionality is the resistance. For other kinds of dependence, we find other functions. The graph below shows why Ohms law is approximately valid in a small range of values of the current and the potential difference.

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.

Lets 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 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 proportionality constant is the resistance.

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

• Ohms 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.

A resistor is a term for a resistance whose value does not vary significantly, which allow us to use Ohm’s law.

Voltage-current characteristics are important because we can extract valuable information from them about the resistance and other quantities in different regions. With this information, we can build devices that serve different purposes.

The current-voltage graph or voltage-current graph is the graphical representation of the behaviour of electric current and voltage in a certain circuit or device.

Current is the rate of flow of charge. Voltage is the work done in carrying a unit charge from one point to another. They are not independent and resistance is a quantity that captures their dependence.

Final Current-Voltage Characteristics Quiz

Question

State Ohm’s law.

For a conductor at a constant temperature, the current through it is proportional to the potential difference across it.

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Question

How can we find the resistance in an I-V graph?

We can find the resistance in an I-V graph by dividing one with the gradient of the curve.

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Question

How does the current-voltage curve differ for different elements?

1. For an ohmic conductor, the I-V curve is a straight line passing through the origin.
2. For a semiconductor, the I-V curve is a horizontal curve that goes straight upwards.
3. For a filament lamp, the I-V curve has an ‘S’ shape.

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Question

What are current-voltage characteristics for resistors?

1. The I-V graph for a resistor is always a straight line.
2. The curve always passes through the origin.
3. The current is directly proportional to the potential difference.

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Question

What are the current-voltage characteristics of a filament lamp?

The resistance increases with higher temperature.

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Question

What is a semiconductor diode?

A diode is a device that allows current to flow only in a particular direction.

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Question

Does the diode allow current to flow in both directions?

No, current flows in only one direction.

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Question

What is a solar cell?

A device that converts light energy to electrical energy.

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Question

What is a thermistor?

A component whose resistance changes with the change in temperature.

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Question

Does thermistor resistance always decrease as temperature increases?

There are two types: type A when the current decreases as the temperature increases, and type B when the current increases as the temperature increases.

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Question

Are thermistor voltage-currents similar to the filament lamps curves?

Yes, they are similar to the filament lamp curves.

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Question

What is the main difference between the thermistor voltage-currents and the filament lamps curves?

The curve is steeper.

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Question

What does a solar cell release after being exposed to sunlight?

Electrons.

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Question

What is the mathematical expression for Ohm’s law?

I=V/R.

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