Class 10th Science Chapter 11 – Electricity | Ohm’s Law and V-I Characteristics

⚡ Electricity

Ohm's Law and V-I Characteristics

ओम का नियम एवं V-I अभिलक्षण

Class 10 Science | CBSE + Foundation + Competitive

⚡ Ohm's Law and V-I Characteristics

1. Introduction | परिचय

The relationship between potential difference, current and resistance is one of the most important concepts in electricity.

For many conductors, when physical conditions such as temperature remain constant, the current through the conductor is directly proportional to the potential difference across it.

This relationship is known as Ohm's Law.

यह संबंध विद्युत परिपथ में वोल्टेज, धारा तथा प्रतिरोध के बीच महत्वपूर्ण संबंध बताता है।

2. Ohm's Law | ओम का नियम

Ohm's law states that, at constant temperature and other physical conditions, the current flowing through a conductor is directly proportional to the potential difference applied across it.

V ∝ I

Therefore:

V = IR

where R is the resistance of the conductor.

3. Mathematical Form of Ohm's Law

V = IR

Quantity	Symbol	SI Unit
Potential Difference	V	Volt (V)
Electric Current	I	Ampere (A)
Resistance	R	Ohm (Ω)

From Ohm's law:

I = V/R

R = V/I

4. Meaning of One Ohm

A conductor has a resistance of 1 ohm if a potential difference of 1 volt across it produces a current of 1 ampere through it.

1 Ω = 1 V / 1 A

Thus:

Ω = V/A

5. Conditions for Ohm's Law

Ohm's law is valid when the physical conditions of the conductor remain constant.

• Temperature should remain approximately constant.
• Physical conditions of the conductor should not change significantly.
• The conductor should behave as an ohmic conductor in the range being studied.

Important: Ohm's law is not a universal law for every electrical device. Devices such as diodes and filament lamps can show non-linear V-I behaviour.

6. Experimental Verification of Ohm's Law

To verify Ohm's law, a circuit is arranged using:

• Cell/Battery
• Key/Switch
• Resistor or resistance wire
• Ammeter
• Voltmeter
• Connecting wires

The ammeter measures current through the resistor and the voltmeter measures potential difference across the resistor.

7. Experimental Circuit Diagram

8. Why is Ammeter Connected in Series?

An ammeter measures the current flowing through a component. Therefore the same current that flows through the component must pass through the ammeter.

Hence the ammeter is connected in series.

Current → Ammeter → Series

9. Why is Voltmeter Connected in Parallel?

A voltmeter measures potential difference between two points. Therefore it is connected across the component.

Voltage → Voltmeter → Parallel

10. V-I Relationship

According to Ohm's law:

V = IR

For a fixed resistance:

V ∝ I

Therefore, if voltage is doubled, current also doubles, provided resistance remains constant.

Voltage V	Current I	V/I
1 V	0.2 A	5 Ω
2 V	0.4 A	5 Ω
3 V	0.6 A	5 Ω
4 V	0.8 A	5 Ω

The constant ratio V/I represents resistance.

11. V-I Characteristics of an Ohmic Conductor

Important: If V is plotted on the y-axis and I on the x-axis, the slope of the straight line is resistance:

R = ΔV / ΔI

12. Slope of V-I Graph

For a graph in which potential difference V is on the vertical axis and current I is on the horizontal axis:

Slope = ΔV/ΔI = R

Therefore:

• Steeper V-I graph → Greater resistance.
• Less steep V-I graph → Lower resistance.
• Straight line through origin → Ohmic behaviour.

13. Important Graph Convention

Students often confuse the slope depending on which quantity is plotted on which axis.

If V is on Y-axis and I on X-axis:

Slope = V/I = R

If I is on Y-axis and V on X-axis:

Slope = I/V = 1/R

14. Ohmic Conductor

A conductor/device that obeys Ohm's law over a specified range of voltage and current is called an ohmic conductor.

Its V-I graph is a straight line through the origin, provided the relevant physical conditions remain constant.

Examples can include many metallic conductors under controlled, approximately constant-temperature conditions.

15. Non-Ohmic Conductor

A device that does not show a linear proportional relationship between V and I is called non-ohmic.

Its V-I graph is generally not a straight line.

Examples:

• Diode
• Filament lamp under changing temperature
• Many semiconductor devices

16. Ohmic vs Non-Ohmic V-I Characteristics

17. Why Does a Filament Lamp Become Non-Linear?

As current increases through the filament, the filament becomes very hot. Its temperature changes significantly, which changes the resistance of the filament.

Therefore V is no longer directly proportional to I over the full range, and the V-I graph becomes curved.

For a metallic filament, resistance generally increases as its temperature rises.

18. Resistance from V-I Data

Suppose the following observations are obtained:

V (Volt)	I (Ampere)	R = V/I (Ω)
2	0.5	4
4	1.0	4
6	1.5	4
8	2.0	4

Since V/I remains constant, the conductor obeys Ohm's law in this range and its resistance is 4 Ω.

19. Numerical Examples

Example 1: A resistor of 5 Ω is connected to a 10 V source. Find current.

I = V/R
I = 10/5
I = 2 A

Example 2: A current of 3 A flows through a 4 Ω resistor. Find voltage.

V = IR
V = 3 × 4
V = 12 V

Example 3: A potential difference of 20 V produces 4 A current. Find resistance.

R = V/I
R = 20/4
R = 5 Ω

Example 4: A resistor carries 0.5 A current at 6 V. Find resistance.

R = V/I
R = 6/0.5
R = 12 Ω

Example 5: A resistor has resistance 10 Ω. What current flows at 50 V?

I = V/R
I = 50/10
I = 5 A

20. Effect of Changing Voltage

For a fixed resistance:

Voltage	Current
V	I
2V	2I
3V	3I
V/2	I/2

At constant R:
V ∝ I

21. Effect of Changing Resistance

At constant voltage:

I = V/R

Therefore current is inversely proportional to resistance.

• Resistance increases → Current decreases.
• Resistance decreases → Current increases.

22. 30 MCQs | बहुविकल्पीय प्रश्न

Q1. Ohm's law is represented by:

A. V = IR

B. V = I/R

C. V = R/I

D. I = VR

Answer: A

Q2. The SI unit of resistance is:

A. Volt

B. Ohm

C. Ampere

D. Coulomb

Answer: B

Q3. For an ohmic conductor at constant temperature:

A. V ∝ 1/I

B. V is independent of I

C. V ∝ I

D. V ∝ I²

Answer: C

Q4. One ohm is equal to:

A. A/V

B. V/A

C. V × A

D. A/V²

Answer: B

Q5. The slope of a V-I graph, with V on Y-axis and I on X-axis, gives:

A. Resistance

B. Current

C. Charge

D. Power

Answer: A

Q6. In an I-V graph, with I on Y-axis and V on X-axis, slope is:

A. R

B. R²

C. 1/R

D. V/I

Answer: C

Q7. A straight-line V-I graph through origin indicates:

A. Non-ohmic behaviour

B. Ohmic behaviour

C. Zero current

D. Infinite resistance

Answer: B

Q8. An ammeter is connected:

A. In parallel

B. In series

C. Across the battery only

D. Outside the circuit

Answer: B

Q9. A voltmeter is connected:

A. In series

B. Only with the switch

C. In parallel

D. In the battery terminal wire only

Answer: C

Q10. If V = 20 V and R = 5 Ω, current is:

A. 4 A

B. 5 A

C. 10 A

D. 25 A

Answer: A

Q11. If I = 2 A and R = 6 Ω, voltage is:

A. 3 V

B. 8 V

C. 12 V

D. 18 V

Answer: C

Q12. If V = 12 V and I = 3 A, resistance is:

A. 4 Ω

B. 9 Ω

C. 15 Ω

D. 36 Ω

Answer: A

Q13. Which is generally non-ohmic?

A. Ideal fixed resistor

B. Copper wire under constant conditions

C. Diode

D. Constant resistance wire

Answer: C

Q14. The resistance of a filament lamp changes mainly because:

A. Its temperature changes

B. Its mass disappears

C. Charge is destroyed

D. Voltage becomes zero

Answer: A

Q15. If resistance is constant and voltage doubles, current:

A. Becomes half

B. Doubles

C. Becomes zero

D. Remains same

Answer: B

Q16. If voltage is constant and resistance doubles, current:

A. Doubles

B. Becomes four times

C. Becomes half

D. Remains same

Answer: C

Q17. Which quantity is represented by V/I?

A. Resistance

B. Charge

C. Current

D. Power

Answer: A

Q18. Which graph represents an ohmic conductor?

A. Straight line through origin

B. Circle

C. Random curve

D. Horizontal curve in all conditions

Answer: A

Q19. A 10 Ω resistor connected to 5 V carries:

A. 0.5 A

B. 2 A

C. 5 A

D. 50 A

Answer: A

Q20. Resistance is a measure of opposition to:

A. Current

B. Mass

C. Temperature

D. Time

Answer: A

Q21. Ohm's law requires approximately constant:

A. Physical conditions

B. Charge only

C. Time only

D. Length only

Answer: A

Q22. The unit of current is:

A. Ohm

B. Ampere

C. Volt

D. Watt

Answer: B

Q23. A conductor with V/I = 8 has resistance:

A. 4 Ω

B. 8 Ω

C. 16 Ω

D. 64 Ω

Answer: B

Q24. If a V-I graph becomes steeper, its resistance is:

A. Lower

B. Zero

C. Higher

D. Always unchanged

Answer: C

Q25. In V = IR, if V = 0 and R is finite, I is:

A. Zero

B. Infinite

C. 1 A always

D. R A

Answer: A

Q26. A resistance of 2 Ω carries 3 A. Voltage is:

A. 1.5 V

B. 5 V

C. 6 V

D. 9 V

Answer: C

Q27. Which instrument measures current?

A. Voltmeter

B. Ammeter

C. Barometer

D. Thermometer

Answer: B

Q28. The V-I graph of an ideal ohmic conductor is:

A. Straight and passes through origin

B. Circular

C. Always horizontal

D. Always vertical

Answer: A

Q29. For constant R, the graph of V versus I has:

A. Zero slope

B. Constant slope R

C. Random slope

D. Infinite slope only

Answer: B

Q30. Which statement is correct?

A. All devices obey Ohm's law under all conditions

B. Ohm's law applies under specified constant physical conditions

C. Resistance is always zero

D. Current never depends on voltage

Answer: B

23. 30 Subjective Questions with Answers

2 Marks Q1. State Ohm's law.

At constant temperature and other physical conditions, current through a conductor is directly proportional to potential difference across it. Thus V ∝ I or V = IR.

2 Marks Q2. Define resistance.

Resistance is the opposition offered by a conductor to the flow of electric current. R = V/I.

2 Marks Q3. What is one ohm?

A conductor has resistance 1 Ω if a potential difference of 1 V produces a current of 1 A through it.

2 Marks Q4. Write Ohm's law in mathematical form.

V = IR.

2 Marks Q5. What does the slope of a V-I graph represent?

When V is on the Y-axis and I on the X-axis, slope represents resistance: R = ΔV/ΔI.

3 Marks Q6. Why is an ammeter connected in series?

Because it must measure the current flowing through the component. Therefore the same current must pass through the ammeter.

3 Marks Q7. Why is a voltmeter connected in parallel?

It measures potential difference between two points and is therefore connected across the component.

3 Marks Q8. What is an ohmic conductor?

A conductor that obeys Ohm's law under specified constant physical conditions is called an ohmic conductor.

3 Marks Q9. What is a non-ohmic conductor?

A device whose current is not directly proportional to applied voltage over the relevant range is called non-ohmic.

3 Marks Q10. What is the significance of a straight-line V-I graph?

It indicates a constant V/I ratio, meaning constant resistance, and therefore ohmic behaviour when the line passes through the origin.

4 Marks Q11. Explain Ohm's law with equation.

At constant temperature, V is directly proportional to I. Therefore V = IR, where R is constant resistance.

4 Marks Q12. Explain the V-I characteristics of an ohmic conductor.

The V-I graph is a straight line through the origin. Equal changes in voltage produce proportional changes in current. Its slope V/I gives resistance.

4 Marks Q13. Explain the difference between ohmic and non-ohmic conductors.

Ohmic conductors have a linear V-I relationship under specified conditions. Non-ohmic devices have a non-linear V-I relationship.

4 Marks Q14. Explain the role of temperature in Ohm's law.

The resistance of many conductors changes with temperature. Therefore Ohm's law is tested under approximately constant physical conditions, especially temperature.

4 Marks Q15. Why does the filament lamp show a curved V-I graph?

Its filament becomes hot as current increases. The change in temperature changes its resistance, causing a non-linear V-I relation.

5 Marks Q16. Describe an experiment to verify Ohm's law.

Connect a battery, key, ammeter and resistance wire in series. Connect a voltmeter in parallel across the resistance wire. Vary the applied voltage and record V and I. Calculate V/I for each reading. If V/I remains constant and the V-I graph is a straight line through the origin, Ohm's law is verified.

5 Marks Q17. Derive R = V/I from Ohm's law.

Ohm's law:
V = IR
Dividing both sides by I:
R = V/I.

5 Marks Q18. Explain the slope of a V-I graph.

Slope = change in V / change in I. For an ohmic conductor:
Slope = ΔV/ΔI = R.
Thus a steeper V-I graph represents greater resistance.

5 Marks Q19. Why is Ohm's law not applicable to every electrical device?

Some devices have resistance that changes with voltage, current, temperature or other conditions. Their V-I relation is therefore non-linear.

5 Marks Q20. Explain why a diode is non-ohmic.

The current through a diode does not vary linearly with voltage over its operating range. Its resistance changes with applied voltage and operating conditions, giving a non-linear characteristic.

6 Marks Q21. A resistor of 8 Ω is connected to 24 V. Calculate current.

I = V/R
I = 24/8
I = 3 A

6 Marks Q22. A current of 2.5 A flows through a resistor of 4 Ω. Find potential difference.

V = IR
V = 2.5 × 4
V = 10 V

6 Marks Q23. A 30 V supply produces 5 A current. Find resistance.

R = V/I
R = 30/5
R = 6 Ω

6 Marks Q24. A resistor has 15 Ω resistance and carries 0.4 A current. Find voltage.

V = IR
V = 0.4 × 15
V = 6 V

6 Marks Q25. A 12 V battery is connected to a 3 Ω resistor. Find current.

I = 12/3
I = 4 A

6 Marks Q26. A conductor has 5 V across it and 0.5 A current. Find resistance.

R = 5/0.5
R = 10 Ω

6 Marks Q27. Explain the difference between V-I and I-V graph slopes.

For V on Y-axis and I on X-axis:
Slope = V/I = R.
For I on Y-axis and V on X-axis:
Slope = I/V = 1/R.

6 Marks Q28. Explain why the resistance of a metallic filament changes on heating.

Heating increases the temperature of the metal filament. Increased temperature causes greater opposition to electron movement, so the resistance of the filament generally increases.

6 Marks Q29. How can you identify an ohmic conductor from experimental data?

Calculate V/I for each observation. If the ratio remains constant, the conductor behaves ohmically over that range. A V-I graph will also be a straight line through the origin.

6 Marks Q30. Explain the complete experimental setup for studying V-I characteristics.

Connect the source, key, ammeter and test resistor in series. Connect the voltmeter across the test resistor. Change the applied voltage, record current and voltage, calculate V/I and plot V against I. A straight line through origin indicates ohmic behaviour; a curved graph indicates non-linear behaviour.

24. Assertion–Reason

Q1. Assertion: For an ohmic conductor, V is directly proportional to I at constant temperature.
Reason: Its resistance remains constant in the specified range.

Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.

Q2. Assertion: The slope of a V-I graph gives resistance.
Reason: Slope = ΔV/ΔI.

Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.

Q3. Assertion: An ammeter is connected in parallel.
Reason: An ammeter measures current.

Answer: Assertion is false; Reason is true.

Q4. Assertion: A filament lamp can have a curved V-I characteristic.
Reason: Its temperature and resistance change as current increases.

Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.

Q5. Assertion: All electrical devices obey Ohm's law under all conditions.
Reason: Ohm's law requires specified physical conditions.

Answer: Assertion is false; Reason is true.

25. HOTS | Higher Order Thinking

HOTS 1. Two V-I graphs are straight lines through the origin. Graph A is steeper than Graph B. Which conductor has greater resistance?

When V is on Y-axis and I on X-axis, slope = R. Therefore the steeper graph has greater resistance.

HOTS 2. A student obtains a curved V-I graph for a metal wire. Does this automatically prove that the wire is non-ohmic?

Not necessarily. The physical conditions, especially temperature, may have changed during the experiment. Ohm's law requires approximately constant physical conditions.

HOTS 3. A resistor has 10 Ω resistance. What voltage is needed for 2 A current?

V = IR = 2 × 10 = 20 V.

HOTS 4. A student plots I on Y-axis and V on X-axis and says the slope is resistance. Is this correct?

No. In an I-V graph, slope = I/V = 1/R. Resistance is the reciprocal of the slope.

HOTS 5. Why must the temperature be controlled during an Ohm's law experiment?

Because resistance can change with temperature. If temperature changes, V/I may not remain constant and the experiment may not correctly test Ohm's law.

26. Graph-Based Questions

Q1. A V-I graph is a straight line through the origin. What does it indicate?

The conductor has constant resistance and shows ohmic behaviour in the tested range.

Q2. What does a curved V-I graph indicate?

The V-I relationship is non-linear; the resistance is not constant over the tested range.

Q3. What does greater slope of a V-I graph mean?

Greater resistance, when V is plotted on Y-axis and I on X-axis.

Q4. What does a line through origin represent physically?

It indicates that when voltage is zero, current is zero and V is directly proportional to I over the relevant range.

Q5. If V/I remains 6 Ω for all readings, what can be concluded?

The resistance is constant at 6 Ω and the conductor behaves as an ohmic conductor under those conditions.

27. Diagram Labelling Practice

Identify the following components:

1. Battery
2. Key/Switch
3. Ammeter
4. Resistance wire / Resistor
5. Voltmeter
6. Series connection
7. Parallel connection

Key Point: Ammeter → Series.
Voltmeter → Parallel.

28. CBSE Golden Points ⭐

1. Ohm's law: V = IR.
2. At constant physical conditions, V ∝ I for an ohmic conductor.
3. Resistance R = V/I.
4. SI unit of resistance is ohm (Ω).
5. 1 Ω = 1 V/A.
6. V-I graph for an ohmic conductor is a straight line through origin.
7. When V is Y-axis and I is X-axis, slope = R.
8. When I is Y-axis and V is X-axis, slope = 1/R.
9. Ammeter is connected in series.
10. Voltmeter is connected in parallel.
11. Ohm's law is valid under specified physical conditions.
12. Filament lamp generally shows non-linear V-I behaviour.
13. Diode is a non-ohmic device.
14. For constant R, doubling V doubles I.
15. For constant V, doubling R halves I.

29. Memory Tricks 🧠

⚡ Trick 1 — VIR Triangle

    V
   ─────
   I   R

V = IR
I = V/R
R = V/I

⚡ Trick 2

V on Y, I on X → Resistance.

⚡ Trick 3

Ammeter = Along the circuit = Series

⚡ Trick 4

Voltmeter = Voltage across = Parallel

⚡ Trick 5

Straight line through origin → Ohmic.
Curved line → Non-linear behaviour.

30. One-Minute Revision ⚡

⚡ Ohm's Law: V = IR.

📐 R = V/I.

📊 Ohmic V-I graph = straight line through origin.

📈 V-Y, I-X → slope = R.

📈 I-Y, V-X → slope = 1/R.

🔌 Ammeter → Series.

📟 Voltmeter → Parallel.

🌡️ Temperature change can change resistance.

💡 Filament lamp → generally non-linear V-I characteristic.

🔧 Diode → non-ohmic behaviour.

31. Concept Map

⚡ Potential Difference
↓ 🔌 Current
↓ 📐 Ohm's Law
↓ V = IR
↓ 🧱 Resistance
↓ 📊 V-I Characteristics
↓ 📈 Straight Line
↓ Ohmic Conductor
or
📈 Curved Line
↓ Non-Ohmic Behaviour

32. Final Summary | अंतिम सारांश

Ohm's law gives the relationship between potential difference, current and resistance.

V = IR

For an ohmic conductor at constant physical conditions:

V ∝ I

The resistance is:

R = V/I

A V-I graph for an ohmic conductor is a straight line through the origin. When V is plotted on the Y-axis and I on the X-axis, the slope gives resistance.

Non-ohmic devices show non-linear V-I characteristics because their resistance is not constant over the relevant range.

⚡ V = IR → Voltage, Current and Resistance

⚡ Electricity

Ohm's Law and V-I Characteristics

ओम का नियम एवं V-I अभिलक्षण

Class 10 Science | CBSE + Foundation + Competitive