Electric charge: property of matter. Two types — positive and negative
SI unit of charge: Coulomb (C)
Charge of electron: e = −1.6 × 10⁻¹⁹ C
Coulomb's Law: F = kq₁q₂/r² where k = 9 × 10⁹ Nm²/C²
Electric field E = F/q = kQ/r². Unit: N/C or V/m
Electric field lines: start from +ve, end at −ve charge
Gauss's Law: total electric flux through closed surface = Q_enclosed/ε₀
ε₀ = 8.85 × 10⁻¹² C²/Nm² (permittivity of free space)
Electric dipole moment p = q × 2a (vector, direction from −q to +q)
✅ Digest Answers
Q. State Coulomb's Law.
The force of attraction or repulsion between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. F = kq₁q₂/r². It acts along the line joining the charges.
Q. What is Gauss's Law?
The total electric flux through any closed surface is equal to the total charge enclosed divided by ε₀. φ = Q/ε₀. It is useful for calculating electric field for highly symmetric charge distributions.
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Physics
Chapter 3 — Current Electricity
📌 Key Formulas
Drift velocity: average velocity of electrons in conductor due to electric field. vd = eEτ/m
Current I = nAevd where n = electron density
Ohm's Law: V = IR
Resistivity ρ = RA/L. Unit: Ω·m
Resistivity increases with temperature for metals
EMF: work done by source per unit charge. ε = E + Ir (terminal voltage = EMF − voltage drop)
Kirchhoff's laws: KCL — sum of currents at junction = 0. KVL — sum of EMFs = sum of IR drops in loop
Wheatstone bridge: P/Q = R/S (balanced condition)
Meter bridge: used to find unknown resistance. R/S = l/(100−l)
✅ Digest Answers
Q. State Kirchhoff's Current Law.
The algebraic sum of all currents meeting at any junction in a circuit is zero. ΣI = 0. This is based on conservation of charge — charge cannot accumulate at a junction. Current flowing in = Current flowing out.
Q. What is terminal voltage of a battery?
Terminal voltage = EMF − Internal voltage drop = ε − Ir. When battery is discharging: V = ε − Ir (less than EMF). When charging: V = ε + Ir (more than EMF).
Point defects: Schottky (missing ions), Frenkel (misplaced ions), Interstitial
✅ Digest Answers
Q. Difference between Schottky and Frenkel defect?
Schottky defect: equal number of cations and anions are missing from lattice. Density decreases. Found in ionic solids with similar ion sizes (NaCl). Frenkel defect: an ion leaves its normal site and occupies an interstitial site. Density unchanged. Found where ions have different sizes (AgCl, ZnS).
Q. How many atoms per unit cell in FCC?
FCC has atoms at 8 corners (8 × 1/8 = 1) and 6 face centres (6 × 1/2 = 3). Total = 1 + 3 = 4 atoms per unit cell.
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Chemistry
Chapter 3 — Electrochemistry
📌 Key Points
Electrochemical cell: converts chemical energy to electrical energy
Electrolytic cell: electrical energy drives non-spontaneous reaction
Standard electrode potential: measured against SHE (Standard Hydrogen Electrode)
Cell EMF = E°cathode − E°anode
Nernst equation: E = E° − (RT/nF)ln Q
Faraday's 1st law: mass deposited ∝ quantity of electricity passed
Faraday's 2nd law: masses of substances deposited by same charge are proportional to their equivalent weights
1 Faraday = 96500 C = charge of 1 mole of electrons
✅ Digest Answers
Q. What is a Galvanic cell? Give an example.
A galvanic (voltaic) cell converts chemical energy into electrical energy through a spontaneous redox reaction. Example: Daniell cell — zinc anode dissolves (oxidation) and copper deposits at cathode (reduction). Zn → Zn²⁺ + 2e⁻ (anode), Cu²⁺ + 2e⁻ → Cu (cathode).
Q. State Faraday's first law of electrolysis.
The mass of substance deposited or dissolved at an electrode during electrolysis is directly proportional to the quantity of electricity (charge) passed. m = ZQ = ZIt, where Z is electrochemical equivalent.
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Mathematics
Chapter 5 — Continuity and Differentiability
📌 Key Points & Formulas
f(x) is continuous at x=a if: lim(x→a) f(x) = f(a)
Every differentiable function is continuous. Converse not always true.
Partnership: business owned by two or more persons (partners)
Partnership deed: written agreement between partners
In absence of deed: no salary, no commission, no interest on capital, profit shared equally, interest on loan = 6% p.a.
Fixed capital: capital remains same, adjustments in separate current account
Fluctuating capital: all adjustments made in capital account
Interest on capital: charge against profit (debit P&L appropriation)
Interest on drawings: charge against partner (credit P&L appropriation)
Profit & Loss Appropriation account: shows distribution of profit among partners
Goodwill: premium paid for reputation of firm
✅ Digest Answers
Q. What is Partnership Deed? What does it contain?
Partnership Deed is a written agreement between partners. It contains: names of partners, capital contributed, profit sharing ratio, interest on capital/drawings, salary or commission to partners, rules for admission/retirement/dissolution of firm.
Q. Difference between fixed and fluctuating capital?
Fixed capital: capital amount stays constant. A separate Current Account records drawings, salary, interest etc. Fluctuating capital: all transactions including drawings, interest, salary are recorded in the Capital Account itself. Capital changes every year.
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