Current Electricity

🟢 Lite — Quick Review

Rapid summary for last-minute revision before your exam.

Current Electricity — Key Facts for BUET Ohm’s Law: V = IR; resistance R = ρL/A (resistivity ρ, length L, area A) Kirchhoff’s Current Law (KCL): ΣI at node = 0 Kirchhoff’s Voltage Law (KVL): ΣV around loop = 0 Power: P = VI = I²R = V²/R ⚡ Exam tip: BUET circuit problems always involve KVL and KCL — always identify loops and nodes before writing equations!

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🟡 Standard — Core Study

Standard content for students with a few days to months.

Current Electricity — BUET Study Guide

Electric current: I = Q/t; unit: ampere (A) = coulomb/second Direction: conventional current (positive to negative)

Ohm’s Law: V = IR; R = V/I Linear relationship for ohmic materials

Resistance: R = ρL/A where ρ = resistivity (Ω·m), L = length, A = cross-section area Temperature dependence: R_T = R₀[1 + α(T − T₀)] where α = temperature coefficient

Resistivity of conductors: ρ increases with temperature: ρ_T = ρ₀[1 + α(T − T₀)] For semiconductors: ρ decreases with temperature (negative α)

Power and energy:

• P = VI = I²R = V²/R
• Energy: W = Pt = I²Rt = V²t/R

Series circuit:

• R_eq = R₁ + R₂ + … (same current)
• Current: I = V/R_eq
• Voltage: V_total = V₁ + V₂ + …

Parallel circuit:

• 1/R_eq = 1/R₁ + 1/R₂ + … (same voltage)
• Voltage: V = V₁ = V₂ = …
• Current: I_total = I₁ + I₂ + …

Kirchhoff’s Laws:

• KCL: algebraic sum of currents at any node = 0 (ΣI_in = ΣI_out)
• KVL: algebraic sum of potential changes around any closed loop = 0

EMF and internal resistance: V = ε − Ir where ε = EMF, r = internal resistance Terminal voltage V < EMF when current flows (unless r = 0)

Cell combination:

• Series: ε_eq = ε₁ + ε₂; r_eq = r₁ + r₂
• Parallel (identical cells): ε_eq = ε; r_eq = r/n

Wheatstone Bridge: For balanced bridge (no current through galvanometer): R₁/R₂ = R₃/R₄ or R₁R₄ = R₂R₃

Potentiometer: Measures EMF accurately (no current drawn, so no loading error) ε₁/ε₂ = l₁/l₂ when balance points found

• Key formula: V = IR; P = VI = I²R; R_eq for series: sum; parallel: 1/R_eq = Σ 1/R_i
• Common trap: When internal resistance is present, terminal voltage = ε − Ir, not just ε
• Exam weight: 2–3 questions per exam (8–12 marks); very high weight

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🔴 Extended — Deep Dive

Comprehensive coverage for students on a longer study timeline.

Current Electricity — Comprehensive BUET Notes

Drift velocity: I = nqAv_d where n = charge carrier density, q = charge, A = cross-section, v_d = drift velocity v_d = I/(nqA) Typical v_d: 10⁻⁴ m/s (very slow!)

Current density: J = I/A = nqv_d Vector J = σE where σ = conductivity = 1/ρ

Resistivity and conductivity: σ = 1/ρ; J = σE Ohm’s law in microscopic form: J = σE

Kirchhoff’s mesh analysis:

1. Assign currents to each branch
2. Choose loop directions
3. Write KVL for each independent loop
4. Solve simultaneous equations

Node voltage method:

1. Choose reference node (ground)
2. Write KCL at each node except reference
3. Express currents in terms of node voltages
4. Solve for node voltages

Superposition theorem: For linear circuits: response = sum of responses from each source acting alone Steps: turn off other sources (replace voltage source with short, current source with open), find contribution from each, sum

Thevenin’s theorem: Any linear circuit can be replaced by V_th in series with R_th V_th = open-circuit voltage between terminals R_th = resistance looking into terminals with all sources turned off

Norton’s theorem: Any linear circuit can be replaced by I_n in parallel with R_n I_n = short-circuit current between terminals R_n = same as R_th

Maximum power transfer: Maximum power delivered to load when R_load = R_th P_max = V_th²/(4R_th)

Delta-Wye transformation: For equivalent circuits: R₁₂ = (R_ab R_ac)/(R_ab + R_ac + R_bc) etc. Or reverse: R_ab = (R_a R_b + R_b R_c + R_c R_a)/R_c

Meter sensitivity: Galvanometer converted to voltmeter by adding series resistance R = (V/I_g) − R_g Galvanometer converted to ammeter by adding shunt resistance R = (I_g R_g)/(I − I_g)

Bridge balance condition: When no current through galvanometer: product of opposite resistances equal R₁/R₂ = R₃/R₄

Capacitor in DC circuit:

• Initially: acts as short circuit (uncharged capacitor, V = 0)
• At steady state: acts as open circuit (no current through capacitor branch)
• Time constant: τ = RC

RC circuit: Charging: V = V₀(1 − e^{−t/RC}) Discharging: V = V₀e^{−t/RC} Time constant τ = RC = time to reach 63% of final value

Ammeter and voltmeter errors:

• Ideal ammeter: zero resistance (insert in series)
• Ideal voltmeter: infinite resistance (connect in parallel)
• Loading error: voltmeter draws some current, changing circuit behavior

Joule heating: H = I²Rt = V²t/R = VIt Useful for fuse design, power dissipation

Electromotive force (EMF): Energy per unit charge provided by source ε = dW/dq; unit: volt

Battery efficiency: η = (V/ε) × 100% = (ε − Ir)/ε × 100%

Meter bridge: Uses Wheatstone principle; balance point gives unknown resistance R_x = R × l₁/(100 − l₁) where R is known resistance

Post office box: Uses Wheatstone bridge with variable known resistances

• Remember: V = IR; KVL: sum of voltage drops = 0; KCL: sum of currents at node = 0; Thevenin: V_th with series R_th; maximum power when R_load = R_th
• Previous years: “Find current through each resistor in circuit with 12V battery and 2Ω, 4Ω, 6Ω resistors” [2023 BUET]; “Find Thevenin equivalent between A and B” [2024 BUET]; “10V battery with internal resistance 1Ω connected to 9Ω load. Find terminal voltage” [2024 BUET]

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📊 BUET Admission Exam Essentials

Detail	Value
Questions	Varies by year (~40-50 MCQ)
Time	Usually 2–3 hours
Marks	Varies by section
Subjects	Mathematics (highest weight), Physics, Chemistry
Negative	Usually no negative marking in BUET
Mode	Written + MCQ depending on year

🎯 High-Yield Topics for BUET Physics

• Mechanics (Laws of Motion, Work-Energy, Rotational) — very high weight
• Electrostatics and Current Electricity — very high weight
• Modern Physics (Photoelectric effect, Atoms) — high weight
• Heat and Thermodynamics — medium-high weight
• Optics (Reflection, Refraction) — medium weight

📝 Previous Year Question Patterns

• Current Electricity: 2–3 questions per exam, 8–12 marks
• Common patterns: circuit analysis, KVL/KCL, Thevenin/Norton, power calculations
• Weight: very high — essential for BUET engineering focus

💡 Pro Tips

• Always draw circuit diagram with current directions marked
• For multiple sources, use superposition or Thevenin/Norton
• KVL: go around loop, subtract drops, sum to zero; KCL: currents into node = currents out
• Terminal voltage = ε − Ir when current flows; if no current, V = ε (open circuit)
• For Wheatstone bridge, check if balanced before calculating equivalent resistance

🔗 Official Resources

• BUET Official
• BUET Admission Portal

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