Month of Equations: What Does Ohm’s Law Really Mean?

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Meaning of the Equation:

This equation is followed from Ohm’s law which states that the magnitude of current flowing between two points of a conductor is directly proportional to the potential difference between those points provided the physical conditions such as temperature and pressure remain constant. The constant of proportionality introduced is defined as the resistance of the conductor R.

This equation is pretty simple to understand, as we all have a first encounter with the topics of electric current and Ohm’s law during our high schools. So, I will first give you a brief recap of what Ohm’s law actually is and then some more insights as to how this law helps to find the resistance of a resistor.

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Consider a simple electronic circuit where a conducting wire is connected to a battery  of potential difference ‘V’ Volts. Let the reading depicted by Ammeter is ‘A’ and Voltmeter is ‘V’. Now, if we replace this battery by a another battery of Voltage ‘V1’ which is greater than ‘V’, we find the new readings in the Ammeter and Voltmeter to be ‘A1’ and ‘V1’ respectively. Ohm’s law states that if ‘V1’ is greater than ‘V’, then ‘A1’ shall also be greater than ‘A’ such that the current is increasing with increasing in proportion to an increase in Voltage.

From Ohm’s law, it is clear that the current flowing between two points of a conductor increases with enhancement in the applied voltage but it is noteworthy that the increase in current is may not be equal to an increase in applied voltage.

# For example,  If voltage changes from 1 V to 2 V, the readings in ammeter may not change from 1 A to 2 A, but may change by any other values,  0.5 A to 1 A  (say). This is because of the resistance of the conductor.

Concept of resistance: Resistance is defined as the inherent ability of a resistor to oppose the flow of current through it. Cause of resistance in a circuit are the collisions among free electrons as well as the collisions of electrons with the stationary atoms.

According to today’s equation, we may find the resistance of the conductor whose voltage is when 1 V, corresponding current is 0.5 A, We find its resistance to be 2 Ohm where Ohm is the unit of resistance.

1 Ohm is defined as the resistance of a resistor through which a current of 1 A flows if the applied voltage is 1 V.

Graphical representation of resistance: A lot of students have problems in understanding the graphical representation of resistance. I will try to make you understand it in a simple way:

The mathematical equation for a straight line is given as : y=m x+c, where, c is the y-intercept (the point where this straight line cuts y-axis), y is the ordinate, x are the corresponding abscissa values and m is the  slope of this straight line. Now, compare this equation of straight line with the equation of Ohm’s law– If we consider V to be the ordinate, I to be the abscissa and plot a graph between the corresponding values of voltmeter and ammeter, this gives us a straight line plot between voltage ‘V’ and current ‘I’ which starts from the origin and whose slope gives us the resistance ‘R’ of the resistor given by the V/I.

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Pictorial representation of Ohm’s law for two resistors having different values of resistance.

In the above figure, the green line has more slope and hence depicts a resistor of higher resistance and the purple line due to greater slope, represents a resistor of comparatively lower resistance.

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