Ohm’s Law Explained with Formula, Resistance, and Sample Problems – Class 10 Science

Explore Ohm’s Law for Class 10 Science at Anand Classes. Understand the relationship between voltage, current, and resistance with clear explanations, examples, and practical applications.

Define Ohm’s Law

Ohm’s Law gives a fundamental relationship between electric current and potential difference in a circuit.

📘 Statement of Ohm’s Law:

At constant temperature, the current flowing through a conductor is directly proportional to the potential difference (voltage) across its ends.

Mathematically,
$$I \propto V \quad \text{(at constant temperature)}$$

Or,
$$V \propto I$$
Which gives,
$$V = R \cdot I$$

Where:

• V = Potential difference (in volts)
• I = Current (in amperes)
• R = Resistance (in ohms Ω\OmegaΩ)

🧮 What is Resistance?

• The constant R is called the resistance of the conductor.
• Resistance depends on:
  • Nature of the material
  • Length of the conductor
  • Area of cross-section
  • Temperature

📐 Mathematical Expression of Ohm’s Law

From the equation:
$$V = R \cdot I$$
We can also write:
$$\frac{V}{I} = R $$

This shows that:

The ratio of potential difference to the current is a constant, known as resistance.

🔁 Rearranging the Formula

Using the equation:
$$\frac{V}{I} = R$$

We can derive:

• $V = I \cdot R$
• $I = \frac{V}{R}$
• $R = \frac{V}{I}$

📌 Key Takeaways from Ohm’s Law

• $I \propto V$ → Current increases with an increase in voltage.
• $I \propto \frac{1}{R}$​ → Current decreases if resistance increases.

Ohm’s Law: Q&A Class 10 Science

Q1. What is Ohm’s Law?

Ohm’s law gives a relationship between current and potential difference. It states: At constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.

Q2. How is Ohm’s Law expressed mathematically?

I ∝ V (at constant temperature)

This can be written as: V ∝ I or V = R × I

Q3. How can Ohm’s Law be rearranged?

V / I = R or I = V / R

Q4. What does the equation V/I = R represent?

It is the mathematical expression of Ohm’s law, showing that the ratio of potential difference to current is a constant, known as resistance.

Q5. What can be inferred from the relation I = V/R?

(i) Current is directly proportional to the potential difference.
(ii) Current is inversely proportional to the resistance.

Q6. What happens to the current if potential difference or resistance is changed?

• If potential difference is doubled, the current also doubles.
• If potential difference is halved, current also halves.
• If resistance is doubled, current is halved.
• If resistance is halved, current is doubled.

Q7. What does the strength of electric current in a conductor depend on?

(i) Potential difference across the conductor’s ends
(ii) Resistance of the conductor

⚡ Resistance of a Conductor

Electric current is the flow of electrons through a conductor. As these electrons move, they collide with atoms, ions, and other electrons in the conductor.

➡️ These collisions cause obstruction to the flow of current.
➡️ This opposition to the flow of electric current is called resistance.

Resistance is the property of a conductor that opposes the flow of electric current through it.

🔢 Mathematical Expression of Resistance

The resistance R of a conductor is given by the ratio of the potential difference (V) across its ends to the current (I) flowing through it:

$$R = \frac{V}{I}$$

Where:

• V = Potential Difference (in volts)
• I = Current (in amperes)
• R = Resistance (in ohms Ω\Omega)

📌 Factors Affecting Resistance of a Conductor

The resistance of a conductor depends on the following factors:

• Length (L) of the conductor
  ➤ Longer wires have more resistance
• Thickness or Area of Cross-section (A)
  ➤ Thicker wires have less resistance, thinner wires have more
• Nature of Material
  ➤ Different materials offer different levels of resistance
• Temperature
  ➤ Higher temperature usually increases resistance

Note : the resistance of all pure metals increases on raising the temperature; and decreases on lowering the temperature. But the resistance of alloys like manganin, constantan and nichrome is almost unaffected by temperature

🧪 SI Unit of Resistance: Ohm (Ω)

The SI unit of resistance is ohm, denoted by the Greek symbol Ω\Omega.

📘 Definition of 1 Ohm:

According to Ohm’s law:

$$R = \frac{V}{I}$$

If:

• V = 1 volt
• I = 1 ampere

Then:

$$R = \frac{1\text{ volt}}{1\text{ ampere}} = 1\,\Omega$$

🔹 1 ohm is the resistance of a conductor such that when 1 volt potential difference is applied across its ends, 1 ampere of current flows through it.

✅ Key Formula to Calculate Resistance

Use Ohm’s Law:

$$R = \frac{V}{I}$$
Or rearranged as:

• $V = I \cdot R$
• $I = \frac{V}{R}$

This formula helps us calculate the resistance of a conductor when voltage and current values are known.

Resistance of a Conductor (Q&A) : Class 10 Science

Q8. What is resistance?

The property of a conductor that opposes the flow of electric current is called resistance. It occurs due to collisions between electrons and atoms in the conductor.

Q9. How is resistance mathematically defined?

Resistance = Potential Difference / Current or R = V / I

Q10. What factors affect the resistance of a conductor?

Resistance depends on:

• Length of the conductor
• Thickness (cross-sectional area)
• Nature of material
• Temperature

Q11. What is the SI unit of resistance?

The SI unit of resistance is the ohm (Ω).

Q12. What is 1 ohm?

1 ohm = 1 volt / 1 ampere

So, 1 ohm is the resistance of a conductor such that a potential difference of 1 volt causes a current of 1 ampere to flow through it.

Sample Problems Using Ohm’s Law

Q13. Sample Problem 1:

Question: What is the resistance between two points of a wire carrying 2 A current and 0.1 V potential difference?

Solution:

R = V / I = 0.1 / 2 = 0.05 Ω

Q14. Sample Problem 2:

Question: A circuit has a 24 V battery and a resistor of 60 ohms. What is the current?

Solution:

I = V / R = 24 / 60 = 0.4 ampere

Q15. Sample Problem 3:

Question: An electric iron draws 3.4 A from a 220 V supply. What current will it draw from a 110 V supply?

Solution:

Step 1: Find Resistance
R = V / I = 220 / 3.4 = 64.7 Ω

Step 2: Use R to find new current
I = V / R = 110 / 64.7 = 1.7 ampere

MCQs with Explanations

1. Ohm’s Law states that the current flowing through a conductor is directly proportional to the voltage across it, provided the temperature remains constant.
   • a) True
   • b) False
   • Answer: a) True
   • Explanation: According to Ohm’s Law, I ∝ V when temperature is constant, where I is current and V is voltage.
2. The unit of resistance is:
   • a) Ampere
   • b) Volt
   • c) Ohm
   • d) Coulomb
   • Answer: c) Ohm
   • Explanation: Resistance is measured in ohms, symbolized by the Greek letter Ω.
3. Which of the following factors does NOT affect the resistance of a conductor?
   • a) Material
   • b) Temperature
   • c) Length
   • d) Shape
   • Answer: d) Shape
   • Explanation: Resistance is affected by material, length, and temperature, but not shape.
4. If the resistance of a conductor increases, the current will:
   • a) Increase
   • b) Decrease
   • c) Remain unchanged
   • d) None of the above
   • Answer: b) Decrease
   • Explanation: According to Ohm’s Law I = V / R, if resistance increases, current decreases.
5. The resistance of a conductor is directly proportional to its:
   • a) Length
   • b) Cross-sectional area
   • c) Temperature
   • d) All of the above
   • Answer: a) Length
   • Explanation: Resistance increases with the length of the conductor and decreases with the cross-sectional area.
6. If the voltage across a conductor is doubled and the resistance remains constant, the current will:
   • a) Double
   • b) Half
   • c) Remain the same
   • d) None of the above
   • Answer: a) Double
   • Explanation: According to Ohm’s Law I = V / R, doubling the voltage doubles the current if resistance is constant.
7. The current flowing through a conductor is inversely proportional to its:
   • a) Resistance
   • b) Voltage
   • c) Material
   • d) Temperature
   • Answer: a) Resistance
   • Explanation: According to Ohm’s Law I = V / R, if resistance increases, current decreases, i.e., current is inversely proportional to resistance.
8. What is the relationship between resistance and temperature in most conductors?
   • a) Resistance decreases with an increase in temperature
   • b) Resistance remains the same with a change in temperature
   • c) Resistance increases with an increase in temperature
   • d) Resistance is independent of temperature
   • Answer: c) Resistance increases with an increase in temperature
   • Explanation: In most conductors, resistance increases as the temperature increases.
9. Which of the following is true for a conductor that obeys Ohm’s Law?
   • a) The current and voltage are directly proportional
   • b) The current and voltage are inversely proportional
   • c) The current and resistance are directly proportional
   • d) The voltage and resistance are inversely proportional
   • Answer: a) The current and voltage are directly proportional
   • Explanation: According to Ohm’s Law, I = V / R, indicating direct proportionality between current and voltage.
10. Ohm’s Law can be represented mathematically as:
    • a) V = I × R
    • b) R = V / I
    • c) I = V / R
    • d) All of the above
    • Answer: d) All of the above
    • Explanation: All three equations represent Ohm’s Law in different forms.

Assertion-Reasoning Based MCQs

1. Assertion (A): The resistance of a conductor is directly proportional to its length.
   Reason (R): Longer conductors provide more opposition to the flow of current.
   • a) Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.
   • b) Both Assertion and Reason are true, but Reason is not the correct explanation for Assertion.
   • c) Assertion is true, but Reason is false.
   • d) Assertion is false, but Reason is true.
   • Answer: a) Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.
2. Assertion (A): Ohm’s Law applies only to conductors that have constant resistance.
   Reason (R): The resistance of a conductor depends on factors like temperature and material.
   • a) Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.
   • b) Both Assertion and Reason are true, but Reason is not the correct explanation for Assertion.
   • c) Assertion is true, but Reason is false.
   • d) Assertion is false, but Reason is true.
   • Answer: a) Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.

Do You Know?

1. Do you know?
   The first scientist to observe and formulate Ohm’s Law was Georg Simon Ohm, a German physicist, in 1827.
2. Do you know?
   A superconductor is a material that has zero resistance at very low temperatures, allowing current to flow without any energy loss.
3. Do you know?
   Resistance of conductors is temperature-dependent. For metals, resistance increases with temperature, while for semiconductors, resistance decreases as temperature increases.

Worksheet

1. Calculate the resistance of a wire if the voltage across it is 12V and the current flowing through it is 4A.
2. A copper wire has a resistance of 0.5Ω at 20°C. What will be the resistance at 40°C if the temperature coefficient of resistance of copper is 0.004 per °C?
3. A bulb operates at 100V with a current of 0.5A. What is the resistance of the bulb?

Test Paper with Marks Distribution

Total Marks: 50
Time: 1 Hour

1. Objective Type Questions (MCQs) – 10 questions (1 mark each) = 10 Marks
2. Assertion-Reasoning Type Questions – 5 questions (2 marks each) = 10 Marks
3. Short Answer Questions – 3 questions (3 marks each) = 9 Marks
4. Long Answer Question – 1 question (6 marks) = 6 Marks
5. Numerical Problems – 2 questions (5 marks each) = 10 Marks
6. Do You Know? Facts (General Knowledge Questions) – 2 questions (2 marks each) = 4 Marks

Important Points for Quick Revision

1. Ohm’s Law: V = I × R – The voltage across a conductor is directly proportional to the current flowing through it, provided temperature is constant.
2. Resistance Factors:
   • Length: Directly proportional to resistance.
   • Cross-sectional area: Inversely proportional to resistance.
   • Temperature: Resistance increases with temperature.
3. Unit of Resistance: Ohm (Ω).
4. Calculation: R = V / I, I = V / R, and V = I × R.
5. Application: Ohm’s Law applies to conductors with constant resistance and does not apply to non-ohmic materials.