MIND GROW Magazine

Current Electricity – Stage 1 (JEE Core)

Page 7: Combination of Resistors (Series & Parallel)

1️⃣ Why Combine Resistors?

In real circuits, resistors are rarely isolated. They are connected to:

Control current
Divide voltage
Protect devices

JEE problems test not formulas, but current paths and potential logic.

2️⃣ Resistors in Series

Resistors are in series if:

Same current flows through all
They are connected end-to-end

Equivalent Resistance:
R_eq = R₁ + R₂ + R₃ + ...

Key Properties (Series)

Current is same through each resistor
Total voltage = sum of individual drops
R_eq is always greater than largest resistor

⚠️ JEE Trap:
Same current ≠ same voltage drop (unless resistances are equal).

3️⃣ Voltage Division Rule (Very Important)

In series:

V₁ / V₂ = R₁ / R₂

This rule is frequently hidden inside long JEE circuits.

4️⃣ Resistors in Parallel

Resistors are in parallel if:

Both ends are connected to same two nodes
Voltage across each is same

Equivalent Resistance:
1 / R_eq = 1/R₁ + 1/R₂ + 1/R₃ + ...

Key Properties (Parallel)

Voltage is same across all branches
Current divides inversely proportional to resistance
R_eq is always less than smallest resistor

5️⃣ Current Division Rule

For two resistors in parallel:

I₁ / I₂ = R₂ / R₁

Lower resistance carries higher current.

6️⃣ Special Parallel Results (Must Memorize)

Two equal resistors R in parallel → R/2
n equal resistors R in parallel → R/n

7️⃣ Power Comparison (Hidden JEE Favorite)

Power in resistor:

P = I²R = V²/R

Series → same current → higher R dissipates more power
Parallel → same voltage → lower R dissipates more power

⚠️ JEE Trap:
Never use wrong power formula without checking current/voltage condition.

8️⃣ Comparison Table (Exam Gold)

Feature	Series	Parallel
Current	Same	Divides
Voltage	Divides	Same
Equivalent R	Maximum	Minimum
Failure of one resistor	Circuit breaks	Circuit continues

9️⃣ IIT-JEE Thinking Insight

Golden Rule:
Always identify nodes first → then decide series or parallel. Never rely only on diagram appearance.

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