## Relationship between voltage and current in a resistor?

What is the relationship between voltage and current in a resistor?

Before we can answer this question in more detail we need to understand exactly what is a resistor? The resistance of a resistor is the property that opposes or resists the movement of electrons through it making it necessary to apply an external voltage in order for a current to flow. The electrons that circulate through a resistor or metallic conductor have a certain amount of difficulty in circulating freely as the material resists their movement. The amount of resistance to this flow depends upon the length, the cross-sectional area and the material from which it is made. Electrons in the form of an electrical current will flow better through the conductor if its area is larger and its length is shorter. Then a relationship exists between the shape of the conductor and its ability to pass electrons. This relationship is called “Resistivity”. Resistivity should not be confused with resistance.

A component that is intended to have resistance is called a resistor. Resistors are passive elements within an electrical circuit that is they absorb energy and convert this energy into heat. Also, resistors are bilateral devices meaning that can pass current in both directions. To best describe the resistance of a resistor and hence its characteristics, it is important to define it using Ohm’s Law.

In metallic conductors and also resistors, the current flowing through it is proportional to the applied voltage across it, and for a resistor which is kept constant, doubling the voltage doubles the current and so on. Then the voltage across a conducting material is directly proportional to the current flowing through the material and the relationship between voltage, (V) and current, (I) in which the resistance, (R) is constant is called the constant of proportionality.

This important relationship between the three electrical units (volts, amperes and ohms) was first experimentally determined by Dr Georg Simon Ohm in 1826, and is referred to as ‘Ohm’s Law’. The unit that measures the resistance is called the ohm (Greek symbol Ω ‘omega’). Ohm’s Law is the most fundamental law used in circuit analysis.

By using Ohm’s law it is easy to find the value of each electrical unit V, I and R by knowing the values of the other two components. It provides a simple formula describing the voltage-current relationship for a resistor or any conducting material and this definition is expressed mathematically as:

V = I*R, I = V/R, and R = V/I

Where: I is the current, V is the voltage and R is the resistance.

In its simplest form, Ohm’s law states that the current flowing through a resistor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them. So if the electrical resistance of a conductor is one ohm an applied voltage of one volt will cause a current of one amp to flow. It is also evident that under this law of proportionality, the greater the resistance the less current will flow for a given amount of applied voltage as the ratio is always constant.

However, Ohm’s law only applies to “ohmic materials” that is materials that obey Ohm’s law of proportionality as not all materials follow this V ∝ I relationship.

So, now we understand what Ohm’s Law is, we can say that the relationship between voltage and current in a resistor can be defined as: “the voltage across a resistance = the value of the resistance multiplied by the current flowing through the resistance”.