Question

The graph of voltage versus current for the nonohmic resistor was not a straight line. Describe what happened to the current as the voltage increased, compared to what happened for the ohmic resistor.

Short answer

In a nonohmic resistor, the current varies curvilinearly with voltage, unlike the proportional linear increase seen in an ohmic resistor.

Step-by-step solution

Understand Ohmic Resistors

For an ohmic resistor, according to Ohm's Law, the relationship between voltage \( V \) and current \( I \) is linear. This can be expressed as \( V = IR \), where \( R \) is the constant resistance. A graph of voltage versus current for an ohmic resistor is a straight line, indicating a constant resistance regardless of the voltage.

Understand Nonohmic Resistors

Nonohmic resistors do not follow Ohm's Law. This means that their resistance may change with voltage or current. The voltage-current relationship is not linear, leading to a non-straight graph line, such as a curve or a series of points that don't align.

Analyze Current on Increasing Voltage for Ohmic Resistor

For an ohmic resistor, increasing the voltage results in a proportional increase in current, as the resistance remains constant. This steady increase in current with voltage reflects the linear nature of the graph, where the slope of the line is the resistance \( R \).

Analyze Current on Increasing Voltage for Nonohmic Resistor

In a nonohmic resistor, increasing the voltage does not result in a proportional and straight-line increase in current. The resistance might change, causing the current to increase at a varying rate. This can lead to a curve on the graph instead of a straight line. For example, the current might increase rapidly initially and then slow down, or it might increase slowly at first and then accelerate.

Key concepts

Ohm's Law

Ohm's Law is a fundamental principle in electronics and electrical engineering that describes the relationship between voltage, current, and resistance. It states that the current through a conductor between two points is directly proportional to the voltage across the two points. This relationship can be expressed mathematically as \( V = IR \), where \( V \) is the voltage, \( I \) is the current, and \( R \) is the resistance.

This formula implies that if you increase the voltage while keeping the resistance constant, the current will also increase proportionally. Likewise, if the voltage is decreased, the current will similarly decrease provided the resistance remains unchanged. Ohm's Law is extensively used for calculating one of the three variables (voltage, current, resistance) when the other two are known.

It's important to recognize that Ohm's Law is primarily applicable to ohmic materials—those that maintain a consistent resistance regardless of the applied voltage and current. Understanding this provides a foundation for distinguishing between ohmic and nonohmic conductors.

Voltage-Current Relationship

The relationship between voltage and current is central to understanding electric circuits. In ohmic resistors, this relationship is linear, owing to the direct application of Ohm's Law. A graph of voltage versus current for an ohmic resistor is a straight line, indicating a consistent relationship: as voltage increases, current increases at a steady rate, dictated by the constant resistance.

In contrast, nonohmic resistors do not exhibit this straightforward relationship. As the term suggests, these resistors behave non-linearly, meaning the same increase in voltage does not result in a proportional increase in current. This can result in a curve that varies depending on how the resistance changes with voltage. For instance:

• At low voltages, the current may increase slowly and then accelerate at higher voltages.
• Alternatively, the current might rise quickly with initial increases in voltage but then plateau as the voltage continues to increase.

The complexity of these relationships makes nonohmic resistors interesting in that they often involve semiconductors or materials whose resistance is affected by temperature.

Electrical Resistance

Electrical resistance is a measure of the opposition to the flow of current in a conductor. The concept of resistance is crucial for understanding why some materials follow Ohm's Law and why others do not. In ohmic materials, resistance remains constant no matter the voltage or current passing through it. This timeless property is what leads to a linear voltage-current relationship.

For nonohmic resistors, resistance can change based on several factors, including temperature, frequency of the electrical signal, or even the magnitude of the voltage applied. These variables make nonohmic resistors such as diodes or thermistors distinct, as their behavior doesn't conform to a simple linear rule.

Understanding electrical resistance helps us appreciate how different materials and components can be used to intentionally create desired circuit characteristics. For example, increasing resistance in a circuit can reduce current flow, which is often practical for protecting sensitive components from damage.

So, while the concept of ohmic resistance offers predictability and simplicity, the variety introduced by nonohmic resistance enables a range of applications and functionalities in electronic devices.