MIND GROW Magazine

Electrostatics – Stage 2 (Page 10)

Capacitors with Switches & Charge Sharing

1️⃣ Golden Rule (Tattoo This)

When a switch changes → Charges redistribute → Energy is NOT conserved.

2️⃣ Charge Sharing – Core Concept

When two charged capacitors are connected:

Total charge is conserved
Final voltage becomes same

Q_total (before) = Q_total (after)

3️⃣ Basic Charge Sharing Formula

Two capacitors C₁, C₂ initially at V₁, V₂:

V_final = (C₁V₁ + C₂V₂) / (C₁ + C₂)

👉 This formula alone can solve 80% JEE switch problems.

4️⃣ Most Common JEE Case

One capacitor charged, one uncharged:

V_final = (C₁V₀) / (C₁ + C₂)

⚠️ Final voltage is always LESS than initial voltage.

5️⃣ Energy Loss – Why It Happens?

Initial energy:

U_i = ½ C₁ V₀²

Final energy:

U_f = ½ (C₁ + C₂) V_final²

❌ U_i ≠ U_f

Energy is lost as:

Heat in connecting wire
Radiation

6️⃣ Switch Closed for Long Time

If switch remains closed:

System reaches electrostatic equilibrium
No current flows
Voltages become constant

✔️ Always analyze FINAL steady state.

7️⃣ Multiple Switches (Advanced JEE)

Method:

Analyze circuit BEFORE switch
Freeze charges instantly at switching moment
Re-analyze AFTER switch

⚠️ Never mix before & after states.

8️⃣ Floating Capacitor Trick

If a capacitor is isolated (floating):

Its total charge remains constant
Voltage may change

🔥 Floating capacitor = charge locked.

9️⃣ Typical JEE Trap

Switch opens suddenly:

Charge remains same
Voltage changes instantly

⚠️ Voltage can change without current flow.

🔟 Ultimate Exam Checklist

✔ Identify initial charge ✔ Apply charge conservation ✔ Find final voltage ✔ Check energy loss ✔ Redraw circuit

➡️ What’s Next?

Stage 3 – Page 1:
Capacitors in Electric Fields + Gauss Law Integration (Rank-Boost Topic)

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