Introduction
HSA Notes brings complete, exam-focused solved notes to help Class 11 (1st Year, HSSC-I) students score high marks in their FBISE Physics board exam.
This page covers Unit 11, Electricity, prepared strictly according to the FBISE New Book (NBF) syllabus, Cantab publisher, for the current academic session, covering drift velocity, electric potential, electromotive force and maximum power output, and the variation of resistance with temperature, along with fully solved examples, derivations, MCQs, short and long questions, numericals, and assignments from HSA Notes.
11.1 Drift Velocity
Definition: Drift velocity (v_d) is the average velocity acquired by free electrons in a conductor as a result of an applied electric field, superimposed on their random thermal motion.
Derivation: The relationship between current and drift velocity is given by:
I = n e A vd
where n is the number of free electrons per unit volume, e is the charge on an electron, A is the cross-sectional area of the conductor, and v_d is the drift velocity.
Solved Example: For a copper wire carrying a current I = 1 A, with cross-sectional area A = 10⁻⁶ m² and free electron density n = 8.5 × 10²⁸ m⁻³, the drift velocity is calculated as:
vd = 7.35 × 10⁻⁵ m/s
This surprisingly small value illustrates that individual electrons move very slowly through a conductor, even though the electric signal itself travels almost instantaneously.
Mobility: Drift velocity is also related to the applied electric field through the mobility (μ) of the charge carriers:
vd = μE
More solved numericals on drift velocity, covering different conductors and current values, are included in the full PDF.
11.2 Electric Potential
Definition: Electric potential (V) at a point is defined as the potential energy per unit charge at that point:
ΔV = ΔU / Q
where ΔU is the change in potential energy and Q is the charge. Electric potential is measured in volts (V), where 1 volt = 1 joule per coulomb.
Electron Volt (eV): A commonly used unit of energy in atomic and electrical physics, defined as the energy gained by an electron moving through a potential difference of one volt:
1 eV = 1.6 × 10⁻¹⁹ J
Detailed short questions on electric potential, covering potential difference, potential surfaces, and related concepts, are included in the full PDF.
11.3 Electromotive Force and Maximum Power Output
Electromotive Force (emf): The total energy supplied by a source per unit charge, denoted by ε. Due to the internal resistance (r) of the source, the terminal voltage delivered to an external circuit is always less than the emf:
V = ε − Ir
The current flowing in a simple circuit consisting of a source with internal resistance r connected to an external resistance R is given by:
I = ε / (R + r)
Maximum Power Output: The power delivered to the external resistance R is maximum when R equals the internal resistance r of the source, given by:
P_max = ε² / 4r
Solved Example: For a source with ε = 12 V and internal resistance r = 1 Ω, connected to an external resistance R = 5 Ω, the circuit values are calculated as I = 2 A, terminal voltage V = 10 V, and power delivered P = 20 W. The maximum possible power output for this source occurs when R = 1 Ω (equal to r), giving Pmax = 36 W.
Fully solved assignments applying the maximum power theorem to different circuit values are included in the full PDF.
11.4 Variation of Resistance with Temperature
The resistance of most conductors changes with temperature, and this relationship is given by:
Rd = R₀ [1 + α(T − T₀)]
where R₀ is the resistance at a reference temperature T₀, Rd is the resistance at temperature T, and α is the temperature coefficient of resistance for the material.
Solved Example: A conductor has resistance R₀ = 10 Ω at T₀ = 20°C, with a temperature coefficient α = 0.0039 °C⁻¹. At a temperature of 100°C, the resistance is calculated as:
Rd = 13.12 Ω
Resistivity: The resistance of a conductor also depends on its physical dimensions and the resistivity (ρ) of the material, given by:
R = ρL / A
where L is the length of the conductor and A is its cross-sectional area. Solved MCQs and long questions covering resistivity and temperature dependence of resistance are included in the full PDF.
Additional Topics Covered in the Full PDF
Beyond the sections summarized above, the complete Unit 11 notes from HSA Notes also include full explanations, solved problems, and assignments on:
- Light Dependent Resistor (LDR)
- Thermistor
- Kirchhoff’s Laws (Current Law and Voltage Law)
- Wheatstone Bridge
- Potentiometer
- Practical applications of resistive circuits
HSA Notes Features
- Complete solved MCQs based on the FBISE paper pattern
- Short and long questions with clear, detailed answers
- Solved numericals with full working and correct units
- Solved assignments matching the current session’s syllabus
- Solved derivations and worked examples for every major formula
- Full Unit 11 Electricity notes for Class 11, based on the FBISE NBF course (Cantab publisher), available in PDF form at hsanotes.com
Why This Unit Matters
Electricity is one of the most numerically demanding units in the Class 11 Physics syllabus, requiring fluency in multiple interconnected formulas, from drift velocity and current to emf, terminal voltage, and resistance variation with temperature.
Available Across All FBISE Institutions
These notes are built for students across all FBISE-affiliated institutions, including APS (Army Public School), IMCB Islamabad, F.G. Colleges, Islamabad Model Colleges, Punjab Colleges, Dr. A.Q. Khan Colleges, Fazaia Inter Colleges, IMCG, and Sir Syed Colleges, matching the quality of notes typically provided in these institutions.
About Our Notes
All academic resources are provided free of cost in PDF format, including detailed notes, guides and handouts, solved exercises and assignments, important and review questions, fill-in-the-blanks, and Multiple Choice Questions (MCQs), all prepared to match the official FBISE NBF course syllabus (Cantab publisher) for this session exactly.
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Frequently Asked Questions
What is drift velocity?
Drift velocity is the average velocity acquired by free electrons in a conductor due to an applied electric field, related to current by I = neAv_d.
What is the difference between emf and terminal voltage?
Emf is the total energy supplied per unit charge by a source, while terminal voltage is the actual voltage delivered to an external circuit, which is less than the emf due to the voltage drop across the source’s internal resistance.
When is power output from a source maximum?
Maximum power is delivered to an external circuit when the external resistance R equals the internal resistance r of the source, given by P_max = ε²/4r.
How does resistance change with temperature?
For most conductors, resistance increases with temperature according to R_t = R₀[1 + α(T − T₀)], where α is the material’s temperature coefficient of resistance.
Conclusion
With Unit 11, Electricity, fully covered, Class 11 FBISE students now have a clear understanding of drift velocity, electric potential, emf, maximum power output, and resistance variation with temperature, along with fully solved MCQs, short and long questions, numericals, and assignments for this session. Practice these solved exercises alongside past papers, and consider joining our online classes for guided, exam-focused preparation, to build the accuracy and confidence needed for your board exam.
Best of luck for your Class 11 Physics exam!