# Formula for Ohm’s law of current and Voltage

There are two basic laws of current electricity – one is Ohm’s law and other one is Kirchhoff’s law. Ohm’s law of current electricity gives the simplest relation between the current and the voltage across a resistance. In this article we are going to discuss the statement and the formula for ohm’s law of current and voltage. Also, the graphical plot and the applications will be discussed here. Syllabus for class 10 and class 12 in India covers this topic.

• Statement of Ohm’s law
• Equation or formula for Ohm’s law
• Explanation of Ohm’s law
• Graph for ohm’s law
• Uses of Ohm’s Law
• Limitations of Ohm’s Law

## Definition of Ohm’s law

Here, the definition refers to the statement. Ohm’s law of current electricity states that if the temperature and other physical state remains constant then the current through a conducting wire is directly proportional to the potential difference or the applied voltage across the wire and the proportional constant is equal to the inverse of the resistance of the wire.

## Formula for Ohm’s law

Let V be the applied voltage across a wire of resistance R and thereby the current flow through the wire is I. Then Ohm’s law tells that, $\small {\color{Blue} I\propto V}$

or, $\small {\color{Blue} I=kV}$, where, k is the proportional constant whose value is equal to the inverse of the resistance (R) of the wire. Then we get the formula of Ohm’s law as, $\small {\color{Blue} I=\frac{1}{R}V}$

or, $\small {\color{Blue} V=IR}$……………… (1)

Equation-(1) gives the mathematical equation for Ohm’s law.

## Explanation of Ohm’s law

Ohm’s law gives the relation between current and voltage through a conductor. In the equation-(1) we can see that it also includes the resistance of the conductor. If we apply a voltage of 10 volt across a conductor of resistance 10 ohm, then the current through the conductor is I=V/R or, current I=1 ampere. This is how one can find the current through the resistance or the conductor.

One can think that it is better to say that voltage is proportional to current in the statement. Yes, one can say that, but that will not be perfect one. Because, here the voltage is an independent quantity which is applied externally. But the current flows through the resistance only due to applied voltage. So, current depends on the applied voltage, not the reverse one. That is why, the current is proportional to the voltage.

## Current-Voltage (I-V) graph

From the equation-(1) one can see that the current through the wire increases with the increase in voltage across it. One should use the equation $\small {\color{Blue} I=\frac{1}{R}V}$ to draw current versus voltage graph. Because, voltage is the independent variable and the current is dependable variable. So, we need to vary the voltage along X-axis and the current along Y-axis. Here, we get a Y=mX type equation with slope 1/R which implies a straight line passing through origin.

Then the current versus voltage graph in ohm’s law will give a straight line passing through the origin with the slope inverse of resistance of the wire. The above diagram shows a current versus voltage graph with some experimental data for verification of Ohm’s law practically. Here, the slope of the curve is AB/BC which is the inverse of the resistance of the conductor.

## Uses of Ohm’s equation

Ohm’s law is used to find the current though a resistance when the resistance and the voltage are known. Actually, any of the three physical quantities (I, V and R) can be found if other two are supplied. Also, one can give the definition of resistance of a conductor from the ohm’s law.

## Limitation of Ohm’s law

There is big limitation of ohm’s law. Ohm’s law is not applicable for non-linear circuit components like diode, Transistor etc. It is only applicable for linear circuit elements like resistor, capacitor, inductor etc. The other limitation is that the resistance of the wire changes with the change in temperature which cause uneven change of the current with change in voltage. Therefore, we need to fix the temperature of the conductor.

Homework problems:

1. If 12 volt battery across a wire causes the 8 ampere current flow through the wire then what is the resistance of the wire?
2. Current through a conductor is 5 A when 10 volt battery is connected across it. What will be the current through the conductor if the voltage applied across it is 12 volt?
3. Find the ratio of current to voltage if the resistance of the conductor is 5 ohm.
4. How one can give the definition of resistance of a conductor by using the formula for Ohm’s law?