Ohm’s Law – Statement, Formula and Solved Examples

In this article, we shall discuss Ohm’s law, its statement, formula, applications, and limitations.

Statement of Ohm’s Law

A German physicist, Georg Simon Ohm first discovered the relationship between current, voltage, and resistance for a conductor. This relationship is known as Ohm’s law.

Ohm’s law states that the voltage V across a conductor is directly proportional to the current I flowing through the conductor, provided the physical conditions like temperature, area, length, etc. do not change, i.e.

`\V∝I`

Ohm defined the constant of proportionality for a conductor to be the resistance R. Where the resistance is the measure of opposition offered by the material of the conductor in the path of electric current. Thus, the expression for ohm’s law can also be written as,

`\V=IR"    "…(1)`

The expression in eq. (1) is the mathematical form of Ohm’s law. Ohm’s law can also be expressed in the following three forms,

`\V=IR;"   "I=V/R;"   "R=V/I`

Explanation of Ohm’s Law

To understand Ohm’s law, consider a resistor as shown in the figure. The voltage across the resistor is V volts and the current flowing through the resistor is I amperes. Then, the ratio V/I will be constant and equal to the resistance R of the resistor. Now, if we double the voltage, then according to Ohm’s law, the current will also be doubled to maintain the ratio V/I constant. It may be noted here that if the voltage is measured in volts and current in amperes, then the resistance will be measured in ohms.

Verification of Ohm’s Law by Experiment

We can easily verify Ohm’s law through the following experiment.

Apparatus Required:

A resistor, an ammeter, a voltmeter, a rheostat, a battery, and a switch.

Circuit Diagram:

We are required to arrange all the apparatus as per the following circuit diagram to verify Ohm’s law.

Procedure:

We perform this experiment as described in the following steps-

Step 1 – At starting, the switch (S) is closed and the rheostat is set to give the minimum reading in the ammeter (A) and voltmeter (V).

Step 2 – Now, move the sliding terminal of the rheostat to gradually increase the current in the circuit. During this process, record the value of the current and the corresponding value of the voltage across the resistor. We now have different sets of values of voltage and current.

Step 3 – For each set of values of current and voltage, calculate the ratio V/I. We will find that the ratio V/I is almost the same. Hence, the resistance of the resistor is constant.

Step 4 – When we plot a graph of the current against the voltage, it will be a straight line. This proves that the current through a resistor is directly proportional to the potential difference.

Practical Importance of Ohm’s Law

In practice, we may use Ohm’s law to validate the standard values of circuit components, currents, voltage supplies, etc. For instance, if a measuring instrument measures a current through a device greater than normal, then it indicates that the resistance of the circuit has decreased or the voltage has increased. On the other hand, a current lower than normal indicates that the voltage has decreased or the resistance of the circuit has increased.

Electrical engineers and technicians refer to nameplates of devices to know rated normal voltage and current values. During testing, if they find that customary values do not display on the digital multimeters or any other device, then they use Ohm’s law to determine what part of the circuit is faulty.

Ohm’s Law Triangle

We can make a triangle to remember the different mathematical relations of Ohm’s law as shown in the following figure.

From this triangle, we can calculate the value of voltage, current, and resistance as follows-

• If the value of voltage is asked, and values of current and resistance are given in the problem. Then, to calculate the value of voltage, we multiply the current and resistance.
• If the value of current is asked, and values of voltage and resistance are given. Then, to calculate the value of the current, we divide the voltage by resistance.
• If the value of resistance is asked, and the value of voltage and current are given. Then, to calculate the value of resistance, we simply divide the voltage by the current.

These three bullet points show how ohm’s law triangle is used to determine the values of voltage, current, and resistance.

Applications of Ohm’s Law

Ohm’s law is one of the most basic laws of circuit analysis. The following are some major applications of Ohm’s law-

• Ohm’s law is used to determine the voltage, current, and resistance of an electric circuit.
• Ohm’s law is used to analyze and design different electrical and electronic systems.

Limitations of Ohm’s Law

There are some situations where we cannot use ohm’s law, these are-

• We cannot use Ohm’s law to analyze the circuits containing unilateral circuit elements like diodes, transistors, etc.
• Ohm’s law is also not applicable for non-linear electrical circuits because, for non-linear circuits, the ratio V/I does not remain constant.

Important Points about Ohm’s Law

The following are some important to remember about Ohm’s law-

• Ohm’s law states that the voltage across a conductor is directly proportional to the current flowing through it.
• Ohm’s law can be used to validate the static values of circuit elements like current, voltage supplies, etc.
• Ohm’s law is not a universal circuit law because it applies to linear bilateral (or ohmic) devices only. To analyze the non-linear or unilateral (unohmic) devices, we cannot use ohm’s law.
• Ohm’s law does not apply to semiconductor devices because they are non-linear.

Numerical Example (1) – A 80 Ω resistor has a voltage of 220 V across it. Find the current flowing through the resistor.

Solution – Given data,

`\R=80" "Ω`

`\V=220" V"`

By applying Ohm’s law, we have,

`\"Current",I=V/R`

`\⟹I=220/80=2.75" A"`

Numerical Example (2) – When a voltage of 24 volts is applied across a metallic conductor, a current of 2.4 A flows through it. Find the resistance of the conductor.

Solution – Given data,

`\V=24" V"`

`\I=2.4" A"`

By Ohm’s law, the resistance of the conductor is given by,

`\"Resistance",R=V/I`

`\⟹R=24/2.4=10" Ω"`

Numerical Example (3) – When a battery is connected across a conductor having a resistance of 50 Ω, a current of 2 A flows through it. Find the voltage of the battery.

Solution – Given data,

`\I=2" A"`

`\R=50" "Ω`

Applying Ohm’s law, we get,

`\"Voltage",V=IR`

`\⟹V=2×50=100" "V`

Conclusion

Hence, in this article, we discussed Ohm’s law, its statement, formula, important points, and solved examples. Ohm’s law is the most elementary circuit law which establishes a relationship between the voltage, current, and resistance of a linear bilateral conductor.