Dimensional Formulas of Physical Quantities Used in Electricity | Class 11 Physics | Question-Answer, FAQS, Worksheet, MCQS, Test Paper

Complete Study Material for JEE, NEET, CBSE Board Class 11 Exams

Electricity is a crucial topic in physics, fundamental to various applications and essential for competitive exams like JEE, NEET, and CBSE Board Class 11. This guide covers key concepts, important formulas, multiple-choice questions (MCQs), conceptual questions, FAQs, worksheets, and test papers.

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Physical Quantities, Units, and Dimensions Used in Electricity

S. No	Quantity	Unit	Dimension
1	Electric charge (q)	Coulomb	[M⁰L⁰T¹A¹]
2	Electric current (I)	Ampere	[M⁰L⁰T⁰A¹]
3	Capacitance (C)	Farad	[M⁻¹L⁻²T⁴A²]
4	Electric potential (V)	Volt	[M¹L²T⁻³A⁻¹]
5	Permittivity of free space (ε₀)	Farad/meter	[M⁻¹L⁻³T⁴A²]
6	Dielectric constant (K)	Unitless	[M⁰L⁰T⁰]
7	Resistance (R)	Ohm	[M¹L²T⁻³A⁻²]
8	Resistivity (ρ)	Ohm-meter	[M¹L³T⁻³A⁻²]
9	Self-inductance (L)	Henry	[M¹L²T⁻²A⁻²]
10	Magnetic flux (φ)	Weber	[M¹L²T⁻²A⁻¹]
11	Magnetic induction (B)	Tesla	[M¹L⁰T⁻²A⁻¹]
12	Magnetic Intensity (H)	Ampere/meter	[M⁰L⁻¹T⁰A¹]
13	Magnetic Dipole Moment (M)	Ampere-meter²	[M⁰L²T⁰A¹]
14	Permeability of Free Space (μ₀)	Henry/meter	[M¹L¹T⁻²A⁻²]
15	Surface charge density (σ)	Coulomb/m²	[M⁰L⁻²T¹A¹]
16	Electric dipole moment (p)	Coulomb-meter	[M⁰L¹T¹A¹]
17	Conductance (G) (1/R)	Siemens	[M⁻¹L⁻²T³A²]
18	Conductivity (σ) (1/ρ)	Siemens/meter	[M⁻¹L⁻³T³A²]
19	Current density (J)	Ampere/m²	[M⁰L⁻²T⁰A¹]
20	Intensity of electric field (E)	Volt/meter	[M¹L¹T⁻³A⁻¹]
21	Rydberg constant (R)	m⁻¹	[M⁰L⁻¹T⁰]

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Conceptual Questions with Answers

Q1: What is the significance of permittivity of free space (ε₀)?

A: Permittivity of free space determines how electric fields interact in a vacuum. It appears in Coulomb’s law and affects the strength of electrostatic forces.

Q2: Why is the unit of resistance in ohms (Ω)?

A: Resistance is the ratio of voltage to current (R = V/I), where voltage is in volts and current in amperes, leading to the derived unit ohm (Ω).

Q3: What is the physical meaning of capacitance?

A: Capacitance represents the ability of a system to store charge per unit voltage. It is measured in farads (F).

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Multiple-Choice Questions (MCQs)

Q1: What is the SI unit of electric charge?

(a) Ampere
(b) Coulomb
(c) Volt
(d) Ohm

Answer: (b) Coulomb
Explanation: Electric charge is measured in coulombs (C), which represents the quantity of electricity transported by one ampere in one second.

Q2: The dimension of resistance is:

(a) [M¹L²T⁻³A⁻²]
(b) [M¹L²T⁻²A⁻²]
(c) [M⁰L⁰T¹A¹]
(d) [M⁰L⁰T⁰A¹]

Answer: (a) [M¹L²T⁻³A⁻²]
Explanation: Resistance (R) = Voltage (V) / Current (I), and using dimensional analysis, we derive [M¹L²T⁻³A⁻²].

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Do You Know?

• Ohm’s Law: Voltage (V) = Current (I) × Resistance (R)
• Kirchhoff’s Laws:
  • First Law (Junction Rule): ΣI (in) = ΣI (out)
  • Second Law (Loop Rule): Σ Voltage drops = Σ Voltage gains
• The SI unit of capacitance is named after Michael Faraday.

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Worksheet

Fill in the Blanks

1. The SI unit of electric current is _______.
2. The unit of magnetic flux is _______.
3. Ohm’s Law states that V = ____ × R.
4. The unit of resistivity is _______.

Short Answer Questions

1. Define electrical resistance and its unit.
2. Explain the significance of dielectric constant.
3. What is the relation between electric field (E) and electric potential (V)?

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Test Paper

Section A: Objective (1 mark each)

1. What is the dimensional formula of electric charge?
2. Define the unit of capacitance.

Section B: Short Answer (2 marks each)

3. Derive the formula for electric potential in terms of work done.
4. Differentiate between resistance and resistivity.

Section C: Long Answer (5 marks each)

5. Explain Kirchhoff’s laws with suitable examples.
6. Derive the formula for the energy stored in a capacitor.

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Quick Revision Points

• Charge (q): Measured in coulombs (C)
• Current (I): Flow of charge per unit time, measured in amperes (A)
• Voltage (V): Potential difference between two points, measured in volts (V)
• Resistance (R): Opposition to current flow, measured in ohms (Ω)
• Capacitance (C): Ability to store charge, measured in farads (F)

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Test Your Knowledge (Quiz)

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