Current Electricity & Circuit Analysis
Solve JEE Main Current Electricity PYQs online. Kirchhoff’s laws, meter bridge, potentiometer, drift velocity & maximum power transfer theorem solutions.
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🎯 High-Yield Syllabus Breakdown
These high-frequency concepts account for over 90% of all questions asked in Current Electricity & Circuit Analysis:
- Drift Velocity v_d = J / (ne) & Ohm’s Law Microscopic Form
- Temperature Dependence of Resistance R_T = R₀ (1 + α ΔT)
- Kirchhoff’s Current Law (KCL - Charge) & Voltage Law (KVL - Energy)
- Wheatstone Bridge, Meter Bridge & Potentiometer Principle
- Galvanometer Conversion to Ammeter (Shunt S) & Voltmeter (Series R)
⚡ Essential Formulas & Speed Shortcuts
Formulas and time-saving shortcuts to solve Current Electricity questions in under 45 seconds:
Stretching Wire: When wire is stretched by x%, resistance increases by R ∝ L² (10% length increase gives 21% resistance increase).
Maximum Power Transfer Theorem: Power to load R is maximum when R = r (internal resistance), with P_max = E² / (4r).
Resistor Cube Body Diagonal: R_eq = 5R / 6.
📖 Sample Solved Exam Questions
Preview authentic questions from this chapter with full step-by-step solutions:
💡 View Step-by-Step Solution & Answer
Correct Answer: 21%
- Step 1: When a wire is stretched uniformly, its volume V = A × L remains constant.
- Step 2: Resistance is R = ρ L / A = ρ L² / V. Hence, R is proportional to L².
- Step 3: If length becomes L' = 1.10 L, new resistance is R' = R (1.10)² = 1.21 R.
- Step 4: Percentage increase in resistance = ((R' - R) / R) × 100 = ((1.21 - 1) / 1) × 100 = 21%.
⚡ Speed Tip: For volume-constant stretching: R ∝ L². For small percentage increase x%: %ΔR ≈ 2x%. For 10%: (1.1)² - 1 = 21%.
💡 View Step-by-Step Solution & Answer
Correct Answer: 4 Ω
- Step 1: Balance condition for a meter bridge: X / R = l / (100 - l).
- Step 2: Given balancing length l = 40 cm, so (100 - l) = 60 cm.
- Step 3: Known resistance in right gap R = 6 Ω.
- Step 4: X / 6 = 40 / 60 = 2 / 3 => X = 6 × (2 / 3) = 4 Ω.
⚡ Speed Tip: Meter bridge balance: X = R × l / (100 - l) = 6 × 40 / 60 = 4 Ω.
💡 View Step-by-Step Solution & Answer
Correct Answer: R = r
- Step 1: Power delivered to load resistor R is P = I² R = [E / (R + r)]² R = E² R / (R + r)².
- Step 2: To find condition for maximum power, differentiate P with respect to R: dP/dR = 0.
- Step 3: dP/dR = E² [ (R + r)² - 2R(R + r) ] / (R + r)⁴ = E² (r - R) / (R + r)³ = 0.
- Step 4: This yields R = r (Maximum Power Transfer Theorem), and P_max = E² / (4r).
⚡ Speed Tip: Maximum Power Transfer Theorem: Internal resistance r must match load resistance R (R = r).
❓ Frequently Asked Questions (FAQs)
Which conservation laws govern Kirchhoff’s Rules?
Junction rule (KCL) is based on Conservation of Charge; Loop rule (KVL) is based on Conservation of Energy.