Ohm’s Law: Definition, Formula, and Sample Questions

Ohm’s law: Ohm’s law is one of the fundamental laws in physics that governs electrical and electronic circuits. Ohm’s law is known to be the relation between voltage and current. The law states that the voltage in a conductor is directly proportional to the current through it.

For example, when we increase the number of cells in a torch, the brightness of the bulb increases. On the other hand, when we use the torch for a long time, we observe that the bulb’s brightness decreases gradually. This happens because the current flowing through the bulb of the torch depends on the potential difference applied across it. If students are confused about the exact definition of Ohm’s law and its applications, we’ve included all the details in this article.

State Ohm’s Law

Ohm’s law is a relation between electric current and potential differences. This relationship between current and potential differences was established by the German physicist Georg Simon Ohm \((1787-1854).\)

Ohm’s Law Defination

Ohm’s law states that the current flowing in a circuit is directly proportional to the applied potential difference and inversely proportional to the resistance in the circuit.

If \(I\) is the current flowing through a conducting wire and \(V\) is the potential difference across the ends of the conducting wire, then according to Ohm’s law (At constant temperature):
\(I\propto V\)
\(\Rightarrow V \propto I\)
\(\Rightarrow V \propto IR\)

Magic Triangle of Ohm’s Law

Ohm’s Law – Resistance of a Conductor

\(1\) Ohm is the resistance of conducting wire in which a current of \(1\) ampere flows when a potential difference of \(1\) volt is applied across its ends.

Experimental Verification of Ohm’s Law

Take five or six dry cells, a resistor with terminals \(A\) and \(B,\) a voltmeter, an ammeter, a key (switch), and some connecting wires. Make an electric circuit by connecting all these components accurately but using only one cell as shown in figure (a) given below. Now, close the electric circuit by making use of the key.

The ammeter measures the current \(I\) flowing through the circuit and the voltmeter measures the voltage across the ends of the resistor \(\left( {AB} \right).\) Note the values shown by the ammeter and voltmeter. Now, connect two cells in series, as shown in figure (b), and again note the new readings of the ammeter and voltmeter. According to Ohm’s law, we will find that on increasing the number of cells in series, the voltage across the terminals of the resistor increases and so the current through it increases. Therefore, the readings on the voltmeter and ammeter also increase. Repeat the experiment by connecting the third cell, fourth cell and so on. Note the reading for each case. Now, when we find the ratio voltage to current for each case, we will find that it is almost the same. Hence, we can conclude that the statement of Ohm’s law is valid for a given conductor or resistor where \(R\) is constant.

If we plot the current-voltage graph using these values of current and voltage, we will get a straight line.

Ohmic Materials

Ohm’s law is not a fundamental law. Ohm’s law is applicable for a large number of conductors. These conducting materials are called Ohmic materials. Metals and their alloys are Ohmic materials. An electric circuit made of ohmic material is called a linear circuit.

Non-Ohmic Materials

There are many useful conducting materials and devices which do not comply with Ohm’s law. These are called non-ohmic conductors and they are considered as one of the limitations of Ohm’s law. Vacuum tubes, crystal rectifiers, thermistors, and transistors are examples of non-ohmic materials. These materials and devices show deviation from the linear behaviour of the current-voltage curve. For example, for semiconductor diodes, when the voltage is positive, a large current flows, when voltage is reversed, only a very small current flows. Superconductors have zero resistance, once a current starts to flow through them.

Ohm’s Law – Factors Affecting Resistance

When temperature and other physical conditions remain unchanged, then from Ohm’s law, the resistance of a conductor remains constant. The following are the factor on which the resistance of a conductor depends:

1. Resistance depends on the temperature.
2. Resistance depends on the length of the conductor.
3. Resistance depends on the area of the cross-section of the conductor.
4. Resistance depends on the nature of the material.

Mathematically,
Resistance
\(R\; \propto \frac{L}{A}\)
\(\Rightarrow R = \rho \frac{L}{A}\)
Where \(L\) is the length of the conductor, \(A\) is the area of cross-section of conductor and \(\rho \) is the resistivity of the material of the conductor or specific resistance.

Resistivity or Specific Resistance 

Resistivity is defined as the resistance across the ends of a conducting wire of unit length and unit cross-section. It can be measured in an Ohm-meter.
\(\rho = \frac{{RA}}{L}\)

Electrical Conductance and Conductivity

The reciprocal of resistance is called electrical conductance. It is represented by \(G.\) It can be measured in siemens \((S)\) or inverse ohm \(\left( {{\Omega ^{ – 1}}} \right)\) Conductivity is the reciprocal of resistivity. It is represented by \(\sigma.\) Good conductors of electricity have high conductivity. They offer less resistance to the flow of current through them.

Ohm’s Law holds at Constant Temperature

The resistivity of a conductor depends on temperature. This is because with an increase in temperature the average speed of positive ions increases resulting in a chance of more collision with the electrons causing current. Variation of resistance with temperature is mainly due to variation of resistivity with temperature. According to Ohm’s law, resistance is constant, so Ohm’s law is applied only at a constant temperature.

Ohm’s Law Formula: Power Calculation Using Ohm’s Law

The knowledge of Ohm’s law will help to calculate the value of electric power. Check the formula to calculate power from below:

When the voltage and current values are known:
P = V I

Formula to calculate current, if power and voltage are known:
I = P/ V

Formula to calculate voltage, if power and current are known:
V = P/ I

Ohm’s Law Matrix Table

The voltage/current/resistance/power can be calculated using formulae derived from Ohm’s Law. Check the formulae from the table below:

Ohm’s Law Solved Examples

Q.1. A potential difference of \(15\;{\rm{V}}\) is applied across a wire of unknown resistance. If the current through the wire is \(0.2\;{\rm{A}}\) then what is the resistance of the wire?
Sol:
Given,
Potential difference \({\rm{V}} = 15\;{\rm{V}}\)
Current \(I = 0.2\;{\rm{A}}\)
According to Ohm’s law, the resistance of the wire,
\(R = \frac{V}{I}\)
Substituting the values in the equation we get,
\(R = \frac{{15}}{{0.2}} = 75\;\Omega\)

Q.2. The current through a conductor of resistance \(250\,{\rm{\Omega }}\) is \(3\;{\rm{A}}.\) If we want to double the current, then what potential difference should be applied across the conductor?
Sol:
Given,
Resistance of the conductor, \(R = 250\;\Omega\)
Initial value of current \(= 3\;{\rm{A}}\)
The required value of current, \(I = 6\;{\rm{A}}\)
Using Ohm’s law we can find the required voltage,
\(V = IR = 6\; \times \;250 = 1500\;{\rm{V}}\)

FAQs on Ohm’s Law

The frequently asked questions on Ohm’s law are given below:

Q.1: Write the formula of Ohm’s law.
Ans: If I is the current flowing through a conducting wire of resistance R and V is the potential difference across the ends of the conducting wire, then according to Ohm’s law:
I∝V
or, V=IR

Q.2: State Ohm’s law.
Ans: Ohm’s law states that the current flowing through a conducting wire is directly proportional to the potential difference across its two ends, provided the temperature remains constant.

Q.3: Define the resistance of a conductor.
Ans: Resistance is the opposition offered by a conductor to the flow of current through it. It is reciprocal of conductance.

Q.4: In which condition Ohm’s law is valid?
Ans: Temperature and other physical conditions remain the same, the current flowing through a conductor is proportional to the potential difference across its two ends.

Q.5: What is 1 ohm?
Ans: We will say that the resistance of a given conductor is 1 ohm, only if a 1-ampere current passes through a conductor when a potential difference of 1 volt is applied.

Q.6: What are non-ohmic materials?
Ans: Materials which does not follow Ohm’s law are called non-ohmic materials. When we plot the graph between voltage and current for such materials, the graph will be non-linear. This means the current is not directly proportional to the applied voltage.

Q.7: What are the limitations of Ohm’s law?
Ans: Ohm’s law is not valid for semiconductors and unilateral networks which has devices like diodes because they allow the unidirectional flow of current.

Learn at Embibe

The concept of Ohm’s Law is usually introduced in Class 10. Also, a few concepts of Ohm’s law are also explained in Class 12. Thus to help you understand all the concepts of Class 10 to Class 12, Embibe offers Mock Test and Practice Questions. Thus Students of Class 10 to Class 12 can solve Practice Questions or attempt 10 Mock Tests on Embibe for which will serve you as a great help in your exam preparation.

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