Electric Potential and Potential Difference, Explanation, Formula, Units, Solved Examples, MCQs, Worksheet

ANAND CLASSES Study Material and Notes to learn the detailed concepts of Electric Potential and Potential Difference with definitions, formulas, examples, and visual aids. Perfect for CBSE, JEE, and NEET students.

🔷 Concept of Electric Field

“When a small positive test charge is placed in the electric field due to another charge, it experiences a force.”

• Every electric charge creates an electric field around itself.
• When you place another charge (called a test charge) in this field, it experiences a force:
  • Attraction if opposite charge.
  • Repulsion if like charge.

🧠 Example: Think of the Sun (main charge) and a small satellite (test charge). The Sun exerts a gravitational force on the satellite, just like an electric field exerts force on a test charge.

🔷 Work is Required Against Repulsion

“So, work has to be done on the positive test charge to move it against this force of repulsion.”

• If the source charge is also positive, the test charge gets repelled.
• To move the test charge closer to the main charge, we must apply force (i.e., do work) against this repulsion.

🛠️ Work done = Force × Distance, just like pushing a ball uphill.

🔷 Definition of Electric Potential

“The electric potential (or potential) at a point in an electric field is defined as the work done in moving a unit positive charge from infinity to that point.”

• Infinity = A place very far away where the influence of any charge is almost zero.
• Electric potential at a point tells us how much energy a unit positive charge gains or loses when moved from infinity to that point.

$$\text{Electric Potential} = \frac{\text{Work Done (W)}}{\text{Charge (Q)}}$$

🧠 Real-life analogy:
Imagine climbing a hill. At the base (infinity), you have no height. As you climb, you gain potential energy. Similarly, as a charge moves into a field, it gains electric potential.

🔷 Units and Meaning

“A potential of 1 volt at a point means that 1 joule of work is done in moving 1 unit positive charge from infinity to that point.”

• 1 volt (V) = 1 joule (J) of work done to move 1 coulomb (C) of charge.

$$V = \frac{W}{Q} \quad \text{or} \quad 1\,V = 1\,J/C$$

🔋 Potential Difference

🔷 Definition:

“The difference in electric potential between two points is known as potential difference.”

Potential Difference (V) between two points is the work done in moving a unit positive charge from one point to another.

$$\text{Potential Difference} = \frac{\text{Work Done (W)}}{\text{Charge (Q)}}$$

It tells us how much more or less energy per unit charge is available at one point compared to another.

✅ SI Unit of Potential Difference

$$1 \, \text{Volt} = \frac{1 \, \text{Joule}}{1 \, \text{Coulomb}}$$

📏 Other Units and Their Relations

🧠 Real-life analogy:
Think of water flowing between two tanks – water flows from higher potential energy (higher tank) to lower potential energy (lower tank). Similarly, electric current flows from higher to lower potential.

🔷 Formula and Meaning

“Potential difference between two points in an electric circuit is defined as the amount of work done in moving a unit charge from one point to the other point.”

$$V = \frac{W}{Q}$$

Where:

• V = Potential Difference (in Volts)
• W = Work done (in Joules)
• Q = Charge moved (in Coulombs)

🔷 Interpretation of 1 Volt

“1 volt = 1 joule of work done to move 1 coulomb of charge”

So, $$V = \frac{1\,J}{1\,C} = 1\,J \cdot C^{-1}$$

🧠 Every time a charge flows, it gains or loses energy depending on the potential difference.

🔧 Voltmeter – Instrument Used to Measure Potential Difference

🔷 Working Principle:

“The potential difference is measured by means of an instrument called voltmeter.”

A voltmeter measures voltage (potential difference) between two points.

A Voltmeter always connected in parallel with the circuit because it compares potentials at two different points without affecting the main current flow.

🔷 Why High Resistance?:

"A voltmeter has high resistance so that it takes a negligible current from the circuit."

• It should not interfere with the actual circuit.
• High resistance ensures very little current flows through the voltmeter itself.

🧮 Sample Problems (Explained)

✅ Sample Problem 1:

Q: How much work is done in moving a charge of 2 C from 118 V to 128 V?

• $V = 128 - 118 = 10\,V$
• $Q = 2\,C$

Formula: $W = V \times Q = 10 \times 2 = 20\,J$

🟢 Answer: 20 Joules of work is done

✅ Sample Problem 2:

Q: How much energy is given to each coulomb of charge passing through a 6 V battery?

• $V = 6\,V, Q = 1\,C$

Formula: $W = V \times Q = 6 \times 1 = 6\,J$

🟢 Answer: 6 Joules of energy is given per coulomb

❓ Question-Answer Format with FAQs

🟢 Q1. Why is work done to move a charge in an electric field?

A: Because the charge experiences a force due to the field. Work is required to move it against this force.

🟢 Q2. What is meant by unit positive test charge?

A: A very small positive charge used to measure electric potential without affecting the field.

🟢 Q3. How does electric potential relate to electric potential energy?

A:$$\text{Potential Energy (U)} = q \times V$$

Where q is the charge and V is the potential.

🙋 FAQs

🔹 Q: What is the difference between voltage and potential difference?

A: Both are the same. "Voltage" is the common term; "potential difference" is the scientific term.

🔹 Q: Why is voltmeter connected in parallel?

A: So it can measure the difference in potential between two points without changing the circuit current.

🔹 Q: What is the SI unit of electric potential?

A: Volt (V)

🎯 Conceptual Questions with Answers

🟣 Q1. If no work is done in moving a charge, what is the potential difference?

A: Zero, because: $$V = \frac{W}{Q} = \frac{0}{Q} = 0$$

🟣 Q2. What does it mean if potential at a point is negative?

A: It means work is done by the field to bring the charge, indicating attractive interaction (e.g., near a negative charge).

✅ MCQs with Explanations

1. What is the unit of electric potential?

a) Ampere
b) Coulomb
c) Volt ✅
d) Ohm
👉 Explanation: Electric potential is measured in volts, defined as work per unit charge.

2. A 3V battery does ___ joules of work on 1C of charge.

a) 1
b) 2
c) 3 ✅
d) 4
👉 Explanation: $$W = V \times Q = 3 \times 1 = 3\,J$$

3. The voltmeter is connected ___ in a circuit.

a) in series
b) in parallel ✅
c) either a or b
d) none
👉 Explanation: Always in parallel to measure potential difference between two points.

🤔 Do You Know? (Interesting Facts)

• The name "volt" comes from Alessandro Volta, who invented the electric battery.
• The electric eel can generate a voltage up to 600 volts!
• Lightning can produce a voltage of over 1 billion volts!
• Dry cells and batteries provide potential differences (e.g., AA battery ≈ 1.5 V).

📝 Worksheet

Fill in the blanks:

1. The SI unit of electric potential is __________.
2. A voltmeter is connected in __________ across the circuit.
3. Work done to move 1C of charge through 5V is __________ J.
4. 1 volt = __________ joule/coulomb.

Short Answer Questions:

1. Define electric potential and potential difference.
2. Why is the voltmeter connected in parallel?
3. Calculate the work done in moving 4C of charge across 12V.

📊 Test Paper (Marks: 20)

🔹 Section A – MCQs (1 mark each × 5 = 5 marks)

1. Define 1 volt.
2. Voltmeter is connected in...?
3. SI unit of potential difference is...?
4. What is the formula for work done?
5. The energy given by a 6V battery to 2C charge is...?

🔹 Section B – Short Answers (2 marks × 3 = 6 marks)

1. Why is work done to move a charge in an electric field?
2. Difference between electric potential and potential difference?
3. State the relation between work, charge, and potential difference.

🔹 Section C – Long Answer (4 marks × 2 = 8 marks)

1. Explain electric potential with example.
2. A charge of 5 C is moved across a potential difference of 20 V. Find the work done.

🔹 Section D – Fill in the Blanks (0.5 mark × 2 = 1 mark)

1. The SI unit of charge is __________.
2. Electric current flows from __________ potential to __________ potential.

🔄 Quick Revision Points

✅ Electric potential is work done per unit positive charge.
✅ 1 volt = 1 joule / 1 coulomb
✅ Potential difference causes current to flow.
✅ Measured using voltmeter (connected in parallel).
✅ Formula: $V = \frac{W}{Q}$

✅ Work done = V × Q
✅ High resistance in voltmeter avoids circuit disturbance.

🧠 Summary Points